Dispersion-managed solitons in fibre systems and lasers

Nonlinear systems with periodic variations of nonlinearity and/or dispersion occur in a variety of physical problems and engineering applications. The mathematical concept of dispersion managed solitons already has made an impact on the development of fibre communications, optical signal processing and laser science. We overview here the field of the dispersion managed solitons starting from mathematical theories of Hamiltonian and dissipative systems and then discuss recent advances in practical implementation of this concept in fibre-optics and lasers.

[1]  S.K. Turitsyn,et al.  Novel approaches to numerical modeling of periodic dispersion-managed fiber communication systems , 2000, IEEE Journal of Selected Topics in Quantum Electronics.

[2]  M. Fermann,et al.  230-kW peak power femtosecond pulses from a high power tunable source based on amplification in Tm-doped fiber. , 2005, Optics express.

[3]  V. Zakharov,et al.  Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media , 1970 .

[4]  Elena G. Shapiro,et al.  Variational Approach to the Design of Optical Communication Systems with Dispersion Management , 1998 .

[5]  C J McKinstrie,et al.  Efficient modeling of phase jitter in dispersion-managed soliton systems. , 2002, Optics letters.

[6]  D. Christodoulides,et al.  Vector solitons in birefringent nonlinear dispersive media. , 1988, Optics letters.

[7]  F. Wise,et al.  Observation of antisymmetric dispersion-managed solitons in a mode-locked laser. , 2008, Optics letters.

[8]  O. Okhotnikov,et al.  All-fiber ytterbium soliton mode-locked laser with dispersion control by solid-core photonic bandgap fiber. , 2006, Optics express.

[9]  Yan‐Chow Ma,et al.  The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation , 1979 .

[10]  Thiab R. Taha,et al.  A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation , 2007, Math. Comput. Simul..

[11]  Wilson Sibbett,et al.  Fast quantum-dot saturable absorber for passive mode-locking of solid-state lasers , 2003, The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003..

[12]  N. J. Smith,et al.  Energy-scaling characteristics of solitons in strongly dispersion-managed fibers. , 1996, Optics letters.

[13]  F. Krausz,et al.  Kerr lens mode locking. , 1992, Optics letters.

[14]  Y. Silberberg,et al.  Generation of pulses shorter than 200 fs from a passively mode-locked Er fiber laser. , 1993, Optics letters.

[15]  Dirk Hundertmark,et al.  Decay Estimates and Smoothness for Solutions of the Dispersion Managed Non-linear Schrödinger Equation , 2008, 0804.3778.

[16]  E. Kuznetsov,et al.  Modulation instability of soliton trains in fiber communication systems , 1999 .

[17]  Nick Doran,et al.  Average soliton dynamics in strongly perturbed systems , 1995 .

[18]  Soliton blueshift in tapered photonic crystal fibers. , 2010, Physical review letters.

[19]  N. Akhmedieva,et al.  Dissipative soliton interactions inside a fiber laser cavity , 2005 .

[20]  H. Haus,et al.  Soliton transmission control. , 1991, Optics letters.

[21]  R. Stolen,et al.  The soliton laser. , 1984, Optics letters.

[22]  W Forysiak,et al.  Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion. , 1998, Optics letters.

[23]  D. Richardson,et al.  Nonlinear tapered holey fibers with high stimulated Brillouin scattering threshold and controlled dispersion , 2007 .

[24]  Dietrich Marcuse,et al.  RMS width of pulses in nonlinear dispersive fibers , 1992 .

[25]  R. Herda,et al.  Environmentally Stable Mode-Locked Fiber Laser With Dispersion Compensation by Index-Guided Photonic Crystal Fiber , 2008, IEEE Photonics Technology Letters.

[26]  S. Turitsyn,et al.  On the theory of chirped optical solitons in fiber lines with varying dispersion , 1998 .

[27]  Alberto Bononi,et al.  Unified analysis of weakly-nonlinear dispersion-managed optical transmission systems using a perturbative approach , 2008 .

[28]  W. E. Stewart,et al.  Solution of boundary-value problems by orthogonal collocation , 1995 .

[29]  U. Ascher,et al.  A collocation solver for mixed order systems of boundary value problems , 1979 .

[30]  S. Namiki,et al.  Sub-200-fs pulsed erbium-doped fiber laser using a carbon nanotube-polyvinylalcohol mode locker , 2006 .

[31]  J. Kutz,et al.  Dispersion-managed breathers with average normal dispersion. , 1998, Optics letters.

[32]  Alexander Apolonski,et al.  Chirped-pulse oscillators: theory and experiment , 2006 .

[33]  E. Yomba Generalized hyperbolic functions to find soliton-like solutions for a system of coupled nonlinear Schrödinger equations , 2008 .

[34]  Hermann A. Haus,et al.  Raman response function of silica-core fibers , 1989, Annual Meeting Optical Society of America.

[35]  V. Shrira,et al.  What makes the Peregrine soliton so special as a prototype of freak waves? , 2010 .

[36]  N. Bogolyubov On the theory of superfluidity , 1947 .

[37]  A Poppe,et al.  Chirped-pulse oscillators: a route to high-power femtosecond pulses without external amplification. , 2004, Optics letters.

[38]  Ben M. Herbst,et al.  Numerical Experience with the Nonlinear Schrödinger Equation , 1985 .

[39]  Sergei K. Turitsyn,et al.  Stabilizing effects of dispersion management , 2001 .

[40]  K. Spatschek,et al.  Path-averaged chirped optical soliton in dispersion-managed fiber communication lines , 1999 .

[41]  M. Ablowitz,et al.  Theoretical and Experimental Dynamics of Nonlinear and Dispersion Managed Solitons in an Ultrashort Pulsed Laser , 2005 .

[42]  M. Suzuki,et al.  General theory of higher-order decomposition of exponential operators and symplectic integrators , 1992 .

[43]  Shu Namiki,et al.  Energy rate equations for mode-locked lasers , 1997 .

[44]  A. Kosevich The crystal lattice , 1999 .

[45]  P. Lushnikov Dispersion-managed soliton in a strong dispersion map limit. , 2001, Optics letters.

[46]  Hermann A. Haus,et al.  Ultrashort-pulse fiber ring lasers , 1997 .

[47]  I. Gabitov,et al.  Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation. , 1996, Optics letters.

[48]  R. Herda,et al.  Dispersion compensation-free fiber laser mode-locked and stabilized by high-contrast saturable absorber mirror , 2004, IEEE Journal of Quantum Electronics.

[49]  G. Agrawal,et al.  Timing jitter in dispersion-managed soliton systems with distributed, lumped, and hybrid amplification , 2002 .

[50]  Alan C. Newell,et al.  Solitons in mathematics and physics , 1987 .

[51]  F Lederer,et al.  Gordon Haus effect in dispersion-managed soliton systems. , 1997, Optics letters.

[52]  Pierre-Andre Belanger,et al.  Erratum: Rms characteristics of pulses in nonlinear dispersive lossy fibers , 1995 .

[53]  Michael J. Connelly,et al.  Semiconductor Optical Amplifiers , 2002 .

[54]  James P. Gordon,et al.  Experimental observation of picosecond pulse narrowing and solitons in optical fibers (A) , 1980 .

[55]  S. Novikov,et al.  Theory of Solitons: The Inverse Scattering Method , 1984 .

[56]  N. Zabusky,et al.  Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States , 1965 .

[57]  H. Haus,et al.  Self-starting additive pulse mode-locked erbium fibre ring laser , 1992 .

[58]  A. Zheltikov,et al.  Dispersion and nonlinear phase-shift compensation in high-peak-power short-pulse fiber laser sources using photonic-crystal fibers , 2008 .

[59]  L. M. Hocking,et al.  On the Nonlinear Response of a Marginally Unstable Plane Parallel Flow to a Two-Dimensional Disturbance , 1972 .

[60]  Alwyn C. Scott,et al.  Nonlinear Science: Emergence and Dynamics of Coherent Structures , 1999 .

[61]  D. H. Peregrine,et al.  Water waves, nonlinear Schrödinger equations and their solutions , 1983, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[62]  U. Keller,et al.  Double-chirped semiconductor mirror for dispersion compensation in femtosecond lasers , 1999 .

[63]  Ferenc Krausz,et al.  Dispersion management for a sub-10-fs, 10 TW optical parametric chirped-pulse amplifier. , 2007, Optics letters.

[64]  R. H. Hardin Application of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations , 1973 .

[65]  F. Wise,et al.  Characterization of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion. , 1993, Optics letters.

[66]  Ian H. White,et al.  Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes , 2010 .

[67]  Diana Anderson,et al.  Variational approach to nonlinear pulse propagation in optical fibers , 1983 .

[68]  D. E. Spence,et al.  60-fsec pulse generation from a self-mode-locked Ti:sapphire laser. , 1991, Optics letters.

[69]  Frédéric Dias,et al.  The Peregrine soliton in nonlinear fibre optics , 2010 .

[70]  Boris A. Malomed,et al.  Soliton Management in Periodic Systems , 2006 .

[71]  Adrian Ankiewicz,et al.  Dissipative solitons : from optics to biology and medicine , 2008 .

[72]  Akihiro Maruta,et al.  Recent Progress in Dispersion-Managed Soliton Transmission Technologies , 1997 .

[73]  Frank W. Wise,et al.  Dissipative solitons in normal-dispersion fiber lasers , 2008 .

[74]  Soliton propagation in a dispersion map with deviation from periodicity , 2005 .

[75]  T. Taha,et al.  Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation , 1984 .

[76]  Frank W. Wise,et al.  Spectral filtering for high-energy mode-locking in normal dispersion fiber lasers , 2008 .

[77]  L. Mollenauer,et al.  Soliton propagation in long fibers with periodically compensated loss , 1985, Annual Meeting Optical Society of America.

[78]  K. Cheng Theory of Superconductivity , 1948, Nature.

[79]  I. Zolotovskii,et al.  Pulse compression in a longitudinally inhomogeneous fiber , 2008 .

[80]  J. Dudley,et al.  Supercontinuum generation in photonic crystal fiber , 2006 .

[81]  H. Haus,et al.  77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser. , 1993, Optics letters.

[82]  Magnus Karlsson,et al.  Wave-breaking-free pulses in nonlinear-optical fibers , 1993 .

[83]  B. Charbonnier,et al.  Reduction of the dispersive wave in periodically amplified links with initially chirped solitons , 1997, IEEE Photonics Technology Letters.

[84]  E. Desurvire,et al.  Erbium‐Doped Fiber Amplifiers: Principles and Applications , 1995 .

[85]  S. Wabnitz,et al.  Strong spectral filtering for a mode-locked similariton fiber laser. , 2010, Optics letters.

[86]  F. W. Wise,et al.  Area theorem and energy quantization for dissipative optical solitons , 2009, 2009 Conference on Lasers and Electro-Optics and 2009 Conference on Quantum electronics and Laser Science Conference.

[87]  Dispersion management in an actively modelocked fiber laser with Kerr nonlinearity , 1999 .

[88]  Knight,et al.  Photonic band gap guidance in optical fibers , 1998, Science.

[89]  W. Kaiser,et al.  Self-focusing of optical beams in absorbing media , 1966 .

[90]  F Lederer,et al.  Soliton interaction in strongly dispersion-managed optical fibers. , 1998, Optics letters.

[91]  Yuji Kodama,et al.  Solitons in optical communications , 1995 .

[92]  V. Sokolov,et al.  The Symmetry Approach to Classification of Integrable Equations , 1991 .

[93]  Boaz Ilan,et al.  Carrier-envelope phase slip of ultrashort dispersion-managed solitons. , 2004, Optics letters.

[94]  Sergei K. Turitsyn,et al.  Asymptotic breathing pulse in optical transmission systems with dispersion compensation , 1997 .

[95]  O. Okhotnikov,et al.  Tapered Fiber Bragg Gratings for Dispersion Compensation in Mode-Locked Yb-Doped Fiber Laser , 2010, IEEE Journal of Quantum Electronics.

[96]  Qianshun Chang,et al.  Difference Schemes for Solving the Generalized Nonlinear Schrödinger Equation , 1999 .

[97]  G. Agrawal,et al.  Dispersion tailoring and soliton propagation in silicon waveguides. , 2006, Optics letters.

[98]  Y Kodama,et al.  Guiding-center soliton in fibers with periodically varying dispersion. , 1991, Optics letters.

[99]  M. Ablowitz,et al.  Multiscale pulse dynamics in communication systems with strong dispersion management. , 1998, Optics letters.

[100]  J. Limpert,et al.  Experimental and numerical study of pulse dynamics in positive net-cavity dispersion modelocked Yb-doped fiber lasers. , 2007, Optics express.

[101]  V. E. Zakharov,et al.  The theory of resonance interaction of wave packets in nonlinear media , 2011 .

[102]  Markus Kunze,et al.  On a variational problem with lack of compactness related to the Strichartz inequality , 2004 .

[103]  E. Kuznetsov,et al.  Stability of stationary waves in nonlinear weakly dispersive media , 1975 .

[104]  S. Wabnitz,et al.  Soliton transmission with periodic dispersion compensation: effects of radiation , 1996, IEEE Photonics Technology Letters.

[105]  Sergei K. Turitsyn,et al.  Physics and mathematics of dispersion-managed optical solitons , 2003 .

[106]  I Hartl,et al.  An optimized Er gain band all-fiber chirped pulse amplification system. , 2004, Optics express.

[107]  M. Ablowitz,et al.  On the solution of a class of nonlinear partial di erence equations , 1977 .

[108]  Markus Kunze,et al.  Ground states for the higher-order dispersion managed NLS equation in the absence of average dispersion , 2005 .

[109]  P M Lushnikov,et al.  Fully parallel algorithm for simulating dispersion-managed wavelength-division-multiplexed optical fiber systems. , 2002, Optics letters.

[110]  F. Kh. Abdullaev,et al.  Solitons in media with random dispersive perturbations , 1999 .

[111]  John Ll Morris,et al.  An investigation into the effect of product approximation in the numerical solution of the cubic nonlinear Schro¨dinger equation , 1988 .

[112]  G. Agrawal,et al.  Raman response function for silica fibers. , 2006, Optics letters.

[113]  Yuri S. Kivshar,et al.  Optical Solitons: From Fibers to Photonic Crystals , 2003 .

[114]  Richard O. Moore,et al.  Pulse propagation in media with deterministic and random dispersion variations , 2002 .

[115]  Andy Chong,et al.  All-normal-dispersion femtosecond fiber laser with pulse energy above 20 nJ. , 2007, Optics letters.

[116]  N. J. Smith,et al.  Enhanced power solitons in optical fibres with periodic dispersion management , 1996 .

[117]  Yuri S. Kivshar,et al.  Dark optical solitons: physics and applications , 1998 .

[118]  L. Melnikov,et al.  Soliton fission management by dispersion oscillating fiber. , 2007, Optics express.

[119]  H Lim,et al.  Control of dispersion in a femtosecond ytterbium laser by use of hollow-core photonic bandgap fiber. , 2004, Optics express.

[120]  J R Taylor,et al.  Optical pulse compression in dispersion decreasing photonic crystal fiber. , 2007, Optics express.

[121]  S. Turitsyn,et al.  Applications of Solitons , 2002 .

[122]  Byoungho Lee,et al.  A fast method for nonlinear Schrodinger equation , 2003 .

[123]  Govind P. Agrawal,et al.  Gordon-Haus timing jitter in dispersion-managed systems with lumped amplification , 2002 .

[124]  Z. Fei,et al.  Numerical simulation of nonlinear Schro¨dinger systems: a new conservative scheme , 1995 .

[125]  T. Lakoba,et al.  Hermite-Gaussian expansion for pulse propagation in strongly dispersion managed fibers , 1998 .

[126]  C. Menyuk,et al.  Dispersion-managed solitons at normal average dispersion. , 1998, Optics letters.

[127]  N. Godbout,et al.  Dynamics of parabolic pulses in an ultrafast fiber laser. , 2006, Optics letters.

[128]  Vadim Zharnitsky,et al.  On sharp Strichartz inequalities in low dimensions , 2006 .

[129]  Sergei K Turitsyn,et al.  Theory of parabolic pulse generation in tapered fiber. , 2007, Optics letters.

[130]  J. Garnier,et al.  Optical solitons in random media , 2005 .

[131]  Gino Biondini,et al.  Phase noise of dispersion-managed solitons , 2009 .

[132]  Andy Chong,et al.  All-normal-dispersion femtosecond fiber laser. , 2006, Optics express.

[133]  Jens Limpert,et al.  Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers. , 2009, Optics letters.

[134]  An iterative numerical method for dispersion-managed solitons , 2005 .

[135]  M. Ablowitz,et al.  Dark and gray strong dispersion-managed solitons. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[136]  J. Gibbon,et al.  Solitons and Nonlinear Wave Equations , 1982 .

[137]  Francesco Matera,et al.  Nonlinear Optical Communication Networks , 1998 .

[138]  M. Ablowitz,et al.  Analytical and Numerical Aspects of Certain Nonlinear Evolution Equations , 1984 .

[139]  J. Soto-Crespo,et al.  Extreme waves that appear from nowhere: On the nature of rogue waves , 2009 .

[140]  M. Radziunas,et al.  On Convergence and Stability of the Explicit Difference Method for Solution of Nonlinear Schrödinger Equations , 1999 .

[141]  Zhipei Sun,et al.  Nanotube–Polymer Composites for Ultrafast Photonics , 2009 .

[142]  Vladimir L. Kalashnikov,et al.  Heavily-chirped solitary pulses in the normal dispersion region: New solutions of the cubic-quintic complex Ginzburg-Landau equation , 2005 .

[143]  Intracavity dynamics in high-power mode-locked fiber lasers , 2010 .

[144]  V. Zakharov,et al.  Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method , 1978 .

[145]  Hirokazu Kubota,et al.  Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains , 1993 .

[146]  S. Nolte,et al.  High-power air-clad large-mode-area photonic crystal fiber laser , 2003, 2003 Conference on Lasers and Electro-Optics Europe (CLEO/Europe 2003) (IEEE Cat. No.03TH8666).

[147]  F. Mitschke,et al.  Chains of temporal dark solitons in dispersion-managed fiber. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[148]  Z. Toroczkai,et al.  Pinning method of pulse confinement in optical fiber with random dispersion , 2002 .

[149]  Todd Kapitula,et al.  Stability of bright solitary-wave solutions to perturbed nonlinear Schro , 1998 .

[150]  S. N. Vlasov,et al.  Averaged description of wave beams in linear and nonlinear media (the method of moments) , 1971 .

[151]  B. Herbst,et al.  Split-step methods for the solution of the nonlinear Schro¨dinger equation , 1986 .

[152]  J. Satsuma,et al.  B Initial Value Problems of One-Dimensional self-Modulation of Nonlinear Waves in Dispersive Media (Part V. Initial Value Problems) , 1975 .

[153]  M. S. Ismail,et al.  Highly accurate finite difference method for coupled nonlinear Schrödinger equation , 2004, Int. J. Comput. Math..

[154]  O. Okhotnikov,et al.  Mode-locked ytterbium fiber laser tunable in the 980-1070-nm spectral range. , 2003, Optics letters.

[155]  H. Haus,et al.  Dispersion-managed solitons as nonlinear Bloch waves , 1999 .

[156]  A. Carena,et al.  Suppression of spurious tones induced by the split-step method in fiber systems simulation , 2000, IEEE Photonics Technology Letters.

[157]  Catherine Sulem,et al.  The nonlinear Schrödinger equation , 2012 .

[158]  James P. Gordon,et al.  Chapter 12 – Solitons in High Bit-Rate, Long-Distance Transmission , 1997 .

[159]  F. Ömer Ilday,et al.  Soliton–similariton fibre laser , 2010 .

[160]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[161]  J. Gibbon,et al.  Collapse in the n‐Dimensional Nonlinear Schrödinger Equation—A Parallel with Sundman's , 1983 .

[162]  M. S. Ismail Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method , 2008, Math. Comput. Simul..

[163]  J. Gordon,et al.  Scheme for the characterization of dispersion-managed solitons. , 1999, Optics letters.

[164]  Stefan Wabnitz,et al.  Pulse interactions and collisions in asymmetric higher-order dispersion managed fiber link , 2000 .

[165]  F. Wise,et al.  High-energy femtosecond stretched-pulse fiber laser with a nonlinear optical loop mirror. , 2002, Optics letters.

[166]  Jian-Qiang Sun,et al.  Numerical study of the soliton waves of the coupled nonlinear Schrödinger system , 2004 .

[167]  Mark P. Robinson,et al.  The solution of nonlinear Schrödinger equations using orthogonal spline collocation , 1997 .

[168]  N. Akhmediev,et al.  Dissipative Solitons in the Complex Ginzburg-Landau and Swift Hohenberg Equations , 2005 .

[169]  C. Finot Dispersion managed self-similar parabolic pulses , 2008 .

[170]  F. Wise,et al.  Spectral filtering for mode locking in the normal dispersive regime. , 2008, Optics letters.

[171]  N. Akhmediev,et al.  Modulation instability and periodic solutions of the nonlinear Schrödinger equation , 1986 .

[172]  S. Coleman,et al.  The Uses of Instantons , 1978 .

[173]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[174]  M. Nakazawa,et al.  Optimizing power extraction in stretched‐pulse fiber ring lasers , 1995 .

[175]  Frank W. Wise,et al.  High‐energy femtosecond fiber lasers based on pulse propagation at normal dispersion , 2008 .

[176]  G. Agrawal,et al.  Impact of dispersion fluctuations on 40-Gb/s dispersion-managed lightwave systems , 2003 .

[177]  Alexander O Korotkevich,et al.  Proof-of-concept implementation of the massively parallel algorithm for simulation of dispersion-managed WDM optical fiber systems. , 2010, Optics letters.

[178]  Averaging for solitons with nonlinearity management. , 2003, Physical review letters.

[179]  W. Kath,et al.  Optimal dispersion maps for wavelength-division-multiplexed soliton transmission. , 1998 .

[180]  Sergei K. Turitsyn,et al.  Dispersion-Managed Solitons and Optimization of the Dispersion Management , 1998 .

[181]  H. Yuen,et al.  Nonlinear deep water waves: Theory and experiment , 1975 .

[182]  Toshihiko Hirooka,et al.  Nonlinear Gain Control of Dispersion-Managed Soliton Amplitude and Collisions , 2000 .

[183]  Self-similar core and oscillatory tails of a path-averaged chirped dispersion-managed optical pulse. , 1998, Optics letters.

[184]  Akihiro Maruta,et al.  On the dispersion managed soliton. , 2000, Chaos.

[185]  Andy Chong,et al.  Self-similar pulse evolution in an all-normal-dispersion laser. , 2010, Physical review. A, Atomic, molecular, and optical physics.

[186]  Q. Chang,et al.  New numerical methods for the coupled nonlinear Schrödinger equations , 2010 .

[187]  P. L. Kelley,et al.  Self-focusing of optical beams , 1965, International Quantum Electronics Conference, 2005..

[188]  Francesco Poletti,et al.  All-solid highly nonlinear singlemode fibers with a tailored dispersion profile. , 2011, Optics express.

[189]  J. C. Newby,et al.  A finite-difference method for solving the cubic Schro¨dinger equation , 1997 .

[190]  Lebedev,et al.  Instantons and intermittency. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[191]  D. Y. Tang,et al.  Dark pulse emission of a fiber laser , 2009, 0910.5799.

[192]  W. Forysiak,et al.  The averaging method for finding exactly periodic dispersion-managed solitons , 2000, IEEE Journal of Selected Topics in Quantum Electronics.

[194]  N. Manton,et al.  Topological Solitons by Nicholas Manton , 2004 .

[195]  GENERALIZED MOMENTUM METHOD TO DESCRIBE HIGH-FREQUENCY SOLITARY WAVE PROPAGATION IN SYSTEMS WITH VARYING DISPERSION , 1998 .

[196]  Cyrus D. Cantrell,et al.  Multiple-vibrational-mode model for fiber-optic Raman gain spectrum and response function , 2002 .

[197]  M. W. Phillips,et al.  SELFSTARTING, PASSIVELY MODELOCKED ERBIUM FIBRE RING LASER BASED ON THE AMPLIFYING SAGNAC SWITCH , 1991 .

[198]  S. Turitsyn BREATHING SELF-SIMILAR DYNAMICS AND OSCILLATORY TAILS OF THE CHIRPED DISPERSION-MANAGED SOLITON , 1998 .

[199]  A. Hasegawa,et al.  Guiding-center soliton in optical fibers. , 1990, Optics letters.

[200]  Cristian Antonelli,et al.  Intracavity pulse dynamics and stability for passively mode-locked lasers. , 2007, Optics express.

[201]  Gulcin M. Muslu,et al.  Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation , 2005, Math. Comput. Simul..

[202]  N. Akhmediev,et al.  Exact first-order solutions of the nonlinear Schrödinger equation , 1987 .

[203]  Sergei K. Turitsyn,et al.  Full length article Optical pulse dynamics in fiber links with dispersion compensation , 1997 .

[204]  Todd Kapitula,et al.  Stability of pulses in the master mode-locking equation , 2002 .

[205]  S. Turitsyn,et al.  Instability and collapse of solitons in media with a defocusing nonlinearity , 1989 .

[206]  Milena Stanislavova,et al.  Regularity of ground state solutions of dispersion managed nonlinear schrödinger equations , 2005 .

[207]  S. L. Musher,et al.  Path-averaged optical soliton in double-periodic dispersion-managed systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[208]  James F. Holt,et al.  Numerical solution of nonlinear two-point boundary problems by finite difference methods , 1964, CACM.

[209]  S. Wabnitz,et al.  Optimization of periodically dispersion compensated breathing soliton transmissions , 1997, IEEE Photonics Technology Letters.

[210]  P. A. Schulz,et al.  Femtosecond passively mode-locked Ti:Al(2)O(3) laser with a nonlinear external cavity. , 1989, Optics letters.

[211]  L. Stenflo,et al.  Nonlinear Schrödinger equation including growth and damping , 1977 .

[212]  U. Keller Ultrafast solid-state lasers , 2000, Conference Digest. 2000 Conference on Lasers and Electro-Optics Europe (Cat. No.00TH8505).

[213]  James P. Gordon,et al.  Solitons in optical fibers , 1987 .

[214]  Vladimir E. Zakharov,et al.  Resonant interaction of wave packets in nonlinear media , 1973 .

[215]  Govind P. Agrawal,et al.  Reduced timing jitter in dispersion-managed light-wave systems through parametric amplification , 2003 .

[216]  P. Petropoulos,et al.  Modelocked laser based on ytterbium doped holey fibre , 2001 .

[217]  D. Miller,et al.  Solid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry-Perot saturable absorber. , 1992, Optics letters.

[218]  P. Roberts,et al.  Demonstration of ultra-flattened dispersion in photonic crystal fibers. , 2002, Optics express.

[219]  A. B. Datseff On the nonlinear schrödinger equation , 2009 .

[220]  Keith J. Blow,et al.  Theoretical description of transient stimulated Raman scattering in optical fibers , 1989 .

[221]  H Kogelnik,et al.  Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3 - 1.7-microm spectral region. , 1980, Optics letters.

[222]  I. Gabitov,et al.  Lie-transform averaging in nonlinear optical transmission systems with strong and rapid periodic dispersion variations , 2000 .

[223]  C R Doerr,et al.  Technique for obtaining high-energy ultrashort pulses from an additive-pulse mode-locked erbium-doped fiber ring laser. , 1994, Optics letters.

[224]  Hanquan Wang,et al.  Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations , 2005, Appl. Math. Comput..

[225]  L. Gagnon Exact traveling-wave solutions for optical models based on the nonlinear cubic-quintic Schrödinger equation , 1989 .

[226]  B. Malomed,et al.  Conditions for stationary pulse propagation in the strong dispersion management regime , 1998 .

[227]  V. Kalashnikov Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[228]  John N. Elgin,et al.  Stochastic perturbations of optical solitons. , 1993, Optics letters.

[229]  F. Wise,et al.  Femtosecond fiber lasers with pulse energies above 10 nJ. , 2005, Optics letters.

[230]  I Bennion,et al.  High-power soliton fiber laser based on pulse width control with chirped fiber Bragg gratings. , 1995, Optics letters.

[231]  I. Zolotovskii,et al.  Pulse compression dynamics in a nonlinear longitudinally inhomogeneous optical fiber , 2008 .

[232]  Philippe Emplit,et al.  Picosecond steps and dark pulses through nonlinear single mode fibers , 1987 .

[233]  P. Petropoulos,et al.  Dispersion-shifted all-solid high index-contrast microstructured optical fiber for nonlinear applications at 1.55 microm. , 2009, Optics express.

[234]  Hermann A. Haus,et al.  All-solid-state femtosecond source at 1.55 μm , 1995 .

[235]  Ferenc Krausz,et al.  Chirped-pulse oscillators for the generation of high-energy femtosecond laser pulses , 2005 .

[236]  P. Tchofo Dinda,et al.  Experimental demonstration of 160-GHz densely dispersion-managed soliton transmission in a single channel over 896 km of commercial fibers. , 2003, Optics express.

[237]  Chi-Wang Shu,et al.  Local discontinuous Galerkin methods for nonlinear Schrödinger equations , 2005 .

[238]  Sergei K Turitsyn,et al.  Dissipative dispersion-managed solitons in mode-locked lasers. , 2009, Optics letters.

[239]  P. Shum,et al.  A novel method for analysis of soliton propagation in optical fibers , 1995 .

[240]  Z. Yoshida Nonlinear Science, , 2004 .

[241]  Taras I. Lakoba Stability analysis of the split-step Fourier method on the background of a soliton of the nonlinear Schrödinger equation , 2010, ArXiv.

[242]  M. Dennis,et al.  High repetition rate figure eight laser with extracavity feedback , 1992 .

[243]  Michael L. Dennis,et al.  Compact sources of ultrashort pulses: Modelocking of all-fiber lasers , 1995 .

[244]  S. Wabnitz,et al.  Pulse generation without gain-bandwidth limitation in a laser with self-similar evolution , 2012, Optics express.

[245]  R. Rajaraman,et al.  Solitons and instantons , 1982 .

[246]  Hemmo Tuovinen,et al.  Dissipative dispersion-managed soliton 2 μm thulium/holmium fiber laser. , 2011, Optics letters.

[247]  I. Ventura Theory of Superfluidity , 1979 .

[248]  Pavel Winternitz,et al.  Symmetry classes of variable coefficient nonlinear Schrodinger equations , 1993 .

[249]  L. Debnath Solitons and the Inverse Scattering Transform , 2012 .

[250]  F. Favre,et al.  Transmission Systems Based on Dispersion-Managed Solitons: Theory and Experiment , 1998 .

[251]  Sergei K. Turitsyn,et al.  The multiple-scale averaging and dynamics of dispersion-managed optical solitons , 1999 .

[252]  Gerard Mourou,et al.  Compression of amplified chirped optical pulses , 1985 .

[253]  V. I. Talanov,et al.  Self Focusing of Wave Beams in Nonlinear Media , 1965 .

[254]  C R Menyuk,et al.  Dispersion-managed solitons in a fiber loop with in-line filtering. , 1997, Optics letters.

[255]  J. Nathan Kutz,et al.  Mode-Locked Soliton Lasers , 2006, SIAM Rev..

[256]  E. Doktorov Dynamics of subpicosecond dispersion-managed soliton in a fibre: a perturbative analysis , 2006, nlin/0605049.

[257]  Guy Moebs,et al.  A multilevel method for the resolution of a stochastic weakly damped nonlinear Schro¨dinger equation , 1998 .

[258]  P. C. Hohenberg,et al.  Fronts, pulses, sources and sinks in generalized complex Ginzberg-Landau equations , 1992 .

[259]  Hermann A. Haus,et al.  Additive pulse mode locking , 1989, Annual Meeting Optical Society of America.

[260]  J. R. Taylor,et al.  Subpicosecond soliton pulse formation from self-mode-locked erbium fibre laser using intensity dependent polarisation rotation , 1992 .

[261]  Shusen Xie,et al.  Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation , 2009 .

[262]  K. Komarov,et al.  Generation of stationary ultra-short pulses by a passive mode-locking solid-state laser , 1986 .

[263]  A. Kosevich The Crystal Lattice: Phonons, Solitons, Dislocations , 1999 .

[264]  J. Nathan Kutz,et al.  Guiding-center pulse dynamics in nonreturn-to-zero (return-to-zero) communications systems with mean-zero dispersion , 1997 .

[265]  C. Menyuk,et al.  Optimization of the split-step Fourier method in modeling optical-fiber communications systems , 2003 .

[266]  H. Keller Numerical Methods for Two-Point Boundary-Value Problems , 1993 .

[267]  J. Fujimoto,et al.  Structures for additive pulse mode locking , 1991 .

[268]  Curtis R. Menyuk,et al.  Calculation of timing and amplitude jitter in dispersion-managed optical fiber communications using linearization , 1999 .

[269]  Sergey A. Babin,et al.  Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg–Landau equation , 2011 .

[270]  S. Turitsyn,et al.  Theory of guiding-center breathing soliton propagation in optical communication systems with strong dispersion management. , 1997, Optics letters.

[271]  I. Aranson,et al.  The world of the complex Ginzburg-Landau equation , 2001, cond-mat/0106115.

[272]  A. Newell,et al.  Swift-Hohenberg equation for lasers. , 1994, Physical review letters.

[273]  G. Fairweather,et al.  On the numerical solution of the cubic Schro¨dinger equation in one space variable , 1993 .

[274]  Pelinovsky Instabilities of dispersion-managed solitons in the normal dispersion regime , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[275]  A. Hasegawa,et al.  High-speed soliton transmission in dense periodic fibers. , 1999, Optics Letters.

[276]  Clemens Heitzinger,et al.  A Note on the Symplectic Integration of the Nonlinear Schrödinger Equation , 2004 .

[277]  Nail Akhmediev,et al.  Stability of the pulselike solutions of the quintic complex Ginzburg-Landau equation , 1996 .

[278]  H. Yoshida Construction of higher order symplectic integrators , 1990 .

[279]  Michael Struwe,et al.  Variational methods: Applications to nonlinear partial differential equations and Hamiltonian systems , 1990 .

[280]  W. Eckhaus Studies in Non-Linear Stability Theory , 1965 .

[281]  H. Haus,et al.  Random walk of coherently amplified solitons in optical fiber transmission. , 1986, Optics letters.

[282]  Pavel Winternitz,et al.  Lie symmetries of a generalised nonlinear Schrodinger equation: I. The symmetry group and its subgroups , 1988 .

[283]  T. Sajavaara,et al.  Self-starting stretched-pulse fiber laser mode locked and stabilized with slow and fast semiconductor saturable absorbers. , 2001, Optics letters.

[284]  M.W.Kalinowski Nonlinear Waves , 2016, 1611.10114.

[285]  J. N. Kutz,et al.  Hamiltonian dynamics of dispersion-managed breathers , 1998 .

[286]  Sergei K. Turitsyn,et al.  Breathing solitons in optical fiber links , 1996 .

[287]  Charalambos Makridakis,et al.  A space-time finite element method for the nonlinear Schröinger equation: the discontinuous Galerkin method , 1998, Math. Comput..

[288]  Non-integrability of equations governing pulse propagation in dispersion-managed optical fibers , 1999 .

[289]  Víctor M. Pérez-García,et al.  Symplectic methods for the nonlinear Schrödinger equation , 1996 .

[290]  Dietmar Kracht,et al.  Sub-60-fs ytterbium-doped fiber laser with a fiber-based dispersion compensation. , 2007, Optics letters.

[291]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[292]  J G Fujimoto,et al.  Generation of 90-nJ pulses with a 4-MHz repetition-rate Kerr-lens mode-locked Ti:Al(2)O(3) laser operating with net positive and negative intracavity dispersion. , 2001, Optics letters.

[293]  T. Driscoll,et al.  Regular Article: A Fast Spectral Algorithm for Nonlinear Wave Equations with Linear Dispersion , 1999 .

[294]  Bülent Karasözen,et al.  Symplectic and multi-symplectic methods for coupled nonlinear Schrödinger equations with periodic solutions , 2007, Comput. Phys. Commun..

[295]  Sergei K. Turitsyn,et al.  Optical rogue waves in telecommunication data streams , 2011 .

[296]  S K Turitsyn,et al.  Vector dark solitons. , 1993, Optics letters.

[297]  F. Wise,et al.  Self-similar evolution of parabolic pulses in a laser. , 2004, Physical review letters.

[298]  U. Keller Recent developments in compact ultrafast lasers , 2003, Nature.

[299]  S. Turitsyn,et al.  Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion. , 1998, Optics letters.

[300]  F. M. Knox,et al.  Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion , 1997 .

[301]  J. Garnier Stabilization of dispersion-managed solitons in random optical fibers by strong dispersion management , 2002 .

[302]  I. Morita,et al.  Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission , 1995 .

[303]  Sergei K. Turitsyn,et al.  Dynamics of self-similar dispersion-managed soliton presented in the basis of chirped Gauss-Hermite functions , 1998 .

[304]  K. Nakkeeran,et al.  A collective variable approach for dispersion-managed solitons , 2001 .

[305]  S. M. Zoldi,et al.  Parallel Implementations of the Split-Step Fourier Method for Solving Nonlinear Schr\ , 1997 .

[306]  Alvaro L. Islas,et al.  Multi-symplectic methods for generalized Schrödinger equations , 2003, Future Gener. Comput. Syst..

[307]  S. Turitsyn,et al.  Dispersion-managed soliton in fiber links with in-line filtering presented in the basis of chirped Gauss–Hermite functions , 1999 .

[308]  B. Malomed,et al.  Propagation of an optical pulse in a fibre link with random dispersion management , 1999, nlin/0012040.

[309]  Alan F. Evans Novel fibers for soliton communications , 1998 .

[310]  Hermann A. Haus,et al.  Stretched-Pulse Additive Pulse Mode-Locking in Fiber , 1994 .

[311]  E. Ippen,et al.  Carrier-envelope phase dynamics of octave-spanning dispersion-managed Ti: sapphire lasers. , 2010, Optics express.

[312]  N. Doran,et al.  Average soliton dynamics and the operation of soliton systems with lumped amplifiers , 1991, IEEE Photonics Technology Letters.

[313]  Thierry Georges,et al.  320 Gbit/s soliton WDM transmission over 1100 km with 100 km dispersion-compensated spans of standard fibre , 1997 .

[314]  G. Agrawal,et al.  Raman amplification in fiber optical communication systems , 2005 .

[315]  David D. Morrison,et al.  Multiple shooting method for two-point boundary value problems , 1962, CACM.

[316]  E. Gross Structure of a quantized vortex in boson systems , 1961 .

[317]  J. R. Taylor,et al.  Optical Solitons: Theory and Experiment , 2005 .

[318]  G. Rowlands,et al.  Nonlinear Waves, Solitons and Chaos , 1990 .

[319]  Uri M. Ascher,et al.  Collocation for two-point boundary value problems revisited , 1986 .

[320]  Guy Millot,et al.  Parabolic pulse generation with active or passive dispersion decreasing optical fibers. , 2007, Optics express.

[321]  Nail Akhmediev,et al.  Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion , 1997 .

[322]  S. Wabnitz,et al.  Average dispersion decreasing densely dispersion-managed fiber transmission systems , 2002, IEEE Photonics Technology Letters.

[323]  P. Lazaridis,et al.  Time-bandwidth product of chirped sech(2) pulses: application to phase-amplitude-coupling factor measurement. , 1995, Optics letters.

[324]  R. Stolen,et al.  Intensity discrimination of optical pulses with birefringent fibers. , 1982, Optics letters.

[325]  Hiroshi Inoue,et al.  Inverse Scattering Method for the Nonlinear Evolution Equations under Nonvanishing Conditions , 1978 .

[326]  S. M. Roberts,et al.  Two-point boundary value problems: shooting methods , 1972 .

[327]  L. Gardner,et al.  B-spline finite element studies of the non-linear Schrödinger equation , 1993 .

[328]  S. Wabnitz,et al.  Stabilisation of dispersion-managed soliton transmissions by nonlinear gain , 1999 .

[329]  I. Duling Subpicosecond all-fibre erbium laser , 1991 .

[330]  Erwan Pincemin,et al.  Nonlinearity management in fiber transmission systems with hybrid amplification , 2004 .

[331]  M. Ablowitz,et al.  Solitons in dispersion-managed mode-locked lasers , 2008 .

[332]  J R Taylor,et al.  Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation. , 2006, Optics express.

[333]  Robert D. Russell,et al.  Collocation Software for Boundary-Value ODEs , 1981, TOMS.

[334]  K. Nozaki,et al.  Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation , 1985 .

[335]  Hasegawa,et al.  Guiding-center soliton. , 1991, Physical review letters.

[336]  S V Chernikov,et al.  Ultrashort-pulse propagation in optical fibers. , 1990, Optics letters.

[337]  W. Kath,et al.  Analysis of enhanced-power solitons in dispersion-managed optical fibers. , 1997, Optics letters.

[338]  T. Newson,et al.  Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation , 1992 .

[339]  Govind P. Agrawal,et al.  Raman-Induced timing jitter in dispersion-managed optical communication systems , 2002 .

[340]  Vladimir E. Zakharov,et al.  On propagation of short pulses in strong dispersion managed optical lines , 1999 .

[341]  H. Haus,et al.  Noise of the stretched pulse fiber laser. I. Theory , 1997 .

[342]  Francesco Calogero,et al.  Spectral Transform and Solitons , 2012 .

[343]  James G. Fujimoto,et al.  Analytic theory of additive pulse and Kerr lens mode locking , 1992 .

[344]  Tian-Shiang Yang,et al.  "Magic" dispersion maps for multichannel soliton transmission , 2000, IEEE Journal of Quantum Electronics.

[345]  John Whitehead,et al.  Finite bandwidth, finite amplitude convection , 1969, Journal of Fluid Mechanics.

[346]  J R Taylor,et al.  Soliton trapping of dispersive waves in tapered optical fibers. , 2009, Optics letters.

[347]  H. Haus Mode-locking of lasers , 2000, IEEE Journal of Selected Topics in Quantum Electronics.

[348]  Gino Biondini,et al.  Importance Sampling for Dispersion-Managed Solitons , 2010, SIAM J. Appl. Dyn. Syst..

[349]  A. Hasegawa,et al.  Feasibility of densely dispersion managed soliton transmission at 160 Gb/s , 2000, IEEE Photonics Technology Letters.

[350]  F. M. Knox,et al.  10-Gbt/s soliton communication systems over standard fiber at 1.55 /spl mu/m and the use of dispersion compensation , 1995 .

[351]  C. Mee,et al.  Structured matrix numerical solution of the nonlinear Schrodinger equation by the inverse scattering transform , 2009 .

[352]  Masataka Nakazawa,et al.  Parabolic pulse generation by use of a dispersion-decreasing fiber with normal group-velocity dispersion. , 2004, Optics letters.

[353]  M. H. Ober,et al.  Characterization of ultrashort pulse formation in passively mode-locked fiber lasers , 1992 .

[354]  T. Georges Soliton interaction in dispersion-managed links , 1998 .

[355]  Shian Zhou,et al.  Divided-pulse Amplification of Ultrashort Pulses , 2006, 2007 Conference on Lasers and Electro-Optics (CLEO).

[356]  Yijiang Chen Dark solitons in dispersion compensated fiber transmission systems , 1999 .

[357]  Thiab R. Taha,et al.  Parallel Split-Step Fourier Methods for the Coupled Nonlinear Schrödinger Type Equations , 2005, The Journal of Supercomputing.

[358]  H. Haus Theory of mode locking with a fast saturable absorber , 1975 .

[359]  F. Kärtner,et al.  Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers , 1996 .

[360]  K. Porsezian,et al.  Nonautonomous Soliton Dispersion Management , 2009, IEEE Journal of Quantum Electronics.

[361]  Michel Remoissenet,et al.  Waves Called Solitons: Concepts and Experiments , 1996 .

[362]  E. Infeld,et al.  Solitary Waves in Plasmas and in the Atmosphere , by V. Petviashvili and O. Pokhotelov, Gordon and Breach, 1992, £50, $90, 248 pages. , 1996, Journal of Plasma Physics.

[363]  S. Kumar Noise suppression using dispersion decreasing fibers for RZ transmission systems , 2004, IEEE Photonics Technology Letters.

[364]  S. Kelly,et al.  Characteristic sideband instability of periodically amplified average soliton , 1992 .

[365]  A High Order Accurate Numerical Scheme for A Class of Schrödinger Equation , 2009 .

[366]  Roger Grimshaw,et al.  Water Waves , 2021, Mathematics of Wave Propagation.

[367]  H. Weitzner,et al.  Perturbation Methods in Applied Mathematics , 1969 .

[368]  V Pervak,et al.  Chirped-pulse amplification of laser pulses with dispersive mirrors. , 2009, Optics express.

[369]  M Horowitz,et al.  Dispersion management in a harmonically mode-locked fiber soliton laser. , 2000, Optics letters.

[370]  Vladimir E. Zakharov,et al.  Stability of periodic waves of finite amplitude on the surface of a deep fluid , 1968 .

[371]  G. Biondini The dispersion-managed Ginzburg–Landau equation and its application to femtosecond lasers , 2008, 0810.2527.

[372]  Akira Hasegawa,et al.  Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion , 1973 .

[373]  M. Burak Erdogan,et al.  EXPONENTIAL DECAY OF DISPERSION MANAGED SOLITONS FOR VANISHING AVERAGE DISPERSION , 2010, 1009.3707.

[374]  Costantino De Angelis,et al.  Noise evolution and soliton internal modes in dispersion-managed fiber systems. , 2003, Optics letters.

[375]  S. Wabnitz,et al.  Role of intra and interchannel cross-phase modulation in higher order fiber dispersion management , 2000, IEEE Photonics Technology Letters.

[376]  I. Bennion,et al.  Environmentally stable high-power soliton fiber lasers that use chirped fiber Bragg gratings. , 1995, Optics letters.

[377]  Yifa Tang,et al.  Symplectic and multi-symplectic methods for the nonlinear Schrodinger equation , 2002 .

[378]  G. Millot,et al.  Self-similarity in ultrafast nonlinear optics , 2007 .

[379]  Michel C. Delfour,et al.  Finite-difference solutions of a non-linear Schrödinger equation , 1981 .

[380]  E. Garmire,et al.  Self-trapping of optical beams , 1966 .

[381]  R. Buczyński Photonic Crystal Fibers , 2004 .

[382]  V Pervak,et al.  Dispersion control over the ultraviolet-visible-near-infrared spectral range with HfO2/SiO2-chirped dielectric multilayers. , 2007, Optics letters.

[383]  D. Tang,et al.  Gain-guided soliton in a positive group-dispersion fiber laser. , 2006, Optics letters.

[384]  Jens Limpert,et al.  Fiber lasers and amplifiers: an ultrafast performance evolution. , 2010, Applied optics.

[385]  F. Lederer,et al.  Optimization of soliton transmissions in dispersion-managed fiber links , 1998 .

[386]  A. Maradudin,et al.  The Baker‐Hausdorff Formula and a Problem in Crystal Physics , 1962 .

[387]  A. Hasegawa Solitons in optical communications , 1995 .

[388]  G. Millot,et al.  Dark-soliton-like pulse-train generation from induced modulational polarization instability in a birefringent fiber. , 1998, Optics letters.

[389]  Jian-Qiang Sun,et al.  Multi-symplectic methods for the coupled 1D nonlinear Schrödinger system , 2003 .

[390]  Sergei K. Turitsyn,et al.  Optical spectral broadening and supercontinuum generation in telecom applications , 2006 .

[391]  U. Keller,et al.  All-in-one dispersion-compensating saturable absorber mirror for compact femtosecond laser sources. , 1995, Optics letters.

[392]  Dmitry Pelinovsky,et al.  Averaging of Dispersion-Managed Solitons: Existence and Stability , 2003, SIAM J. Appl. Math..

[393]  S. Turitsyn,et al.  Evolution and stability of pulse regimes in SESAM-mode-locked femtosecond fiber lasers , 2009, CLEO/Europe - EQEC 2009 - European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference.

[394]  Inverse scattering theory with stochastic initial potentials , 1982 .

[395]  E. Kuznetsov,et al.  Solitons in a parametrically unstable plasma , 1977 .

[396]  Enhanced power breathing soliton in communication systems with dispersion management , 1997 .

[397]  W. Ferguson,et al.  Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train , 1977, Journal of Fluid Mechanics.

[398]  M. Lenner,et al.  Dispersion management in femtosecond laser oscillators with highly dispersive mirrors , 2009, CLEO/Europe - EQEC 2009 - European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference.

[399]  Ben Silver,et al.  Elements of the theory of elliptic functions , 1990 .

[400]  C. McKinstrie Effects of filtering on Gordon–Haus timing jitter in dispersion-managed systems , 2002 .

[401]  R. McLachlan Symplectic integration of Hamiltonian wave equations , 1993 .

[402]  Yuri S. Kivshar,et al.  Dark solitons in nonlinear optics , 1993 .

[403]  Jonathan C. Knight,et al.  Photonic crystal fibres , 2003, Nature.

[404]  A. Polyakov,et al.  Pseudoparticle Solutions of the Yang-Mills Equations , 1975 .

[405]  S K Turitsyn,et al.  Soliton and collapse regimes of pulse generation in passively mode-locking laser systems. , 1995, Optics letters.

[406]  M. Guina,et al.  Femtosecond neodymium-doped fiber laser operating in the 894-909-nm spectral range , 2004, IEEE Photonics Technology Letters.

[407]  Mathematical modelling of nonlinear effects in optical fiber , 2010 .

[408]  B C Thomsen,et al.  Self-similar propagation and amplification of parabolic pulses in optical fibers. , 2000, Physical review letters.

[409]  J. M. Sanz-Serna,et al.  Methods for the numerical solution of the nonlinear Schroedinger equation , 1984 .

[410]  V Pervak,et al.  Chirped mirrors with low dispersion ripple. , 2007, Optics express.

[411]  L. Zhang A HIGH ACCURATE AND CONSERVATIVE FINITE DIFFERENCE SCHEME FOR NONLINEAR SCHRODINGER EQUATION , 2005 .

[412]  Linn F. Mollenauer,et al.  Long-distance soliton propagation using lumped amplifiers and dispersion shifted fiber , 1991 .

[413]  D. Q. Chowdhury,et al.  Intrachannel nonlinear penalties in dispersion-managed transmission systems , 2002 .

[414]  S K Turitsyn,et al.  Reduced-power optical solitons in fiber lines with short-scale dispersion management. , 1999, Optics letters.

[415]  Toshihiko Hirooka,et al.  Managing nonlinearity in strongly dispersion-managed optical pulse transmission , 2002 .

[416]  S. Turitsyn,et al.  Hamiltonian averaging and integrability in nonlinear systems with periodically varying dispersion , 1999 .

[417]  Erwan Pincemin,et al.  Distributed-Raman-amplification effect on pulse interactions and collisions in long-haul dispersion-managed soliton transmissions , 2002 .

[418]  Pavel M. Lushnikov,et al.  Oscillating tails of a dispersion-managed soliton , 2004 .

[419]  V. Kalashnikov,et al.  Chirped-pulse oscillators: a unified standpoint , 2008, 0811.1078.