Breathers and multi-soliton solutions for the higher-order generalized nonlinear Schrödinger equation

Abstract In this paper, the higher-order generalized nonlinear Schrodinger equation, which describes the propagation of ultrashort optical pulse in optical fibers, is analytically investigated. By virtue of the Darboux transformation constructed in this paper, some exact soliton solutions on the continuous wave (cw) background are generated. The following propagation characteristics of those solitons are mainly discussed: (1) Propagation of two types of breathers which delineate modulation instability and bright pulse propagation on a cw background respectively; (2) Two types propagation characteristics of two-solitons: elastic interactions and mutual attractions and repulsions bound solitons. Those results might be useful in the study of ultrashort optical solitons in optical fibers.

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

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

[3]  O. C. Wright.  Homoclinic Connections of Unstable Plane Waves of the Long‐Wave–Short‐Wave Equations , 2006 .

[4]  V. Matveev,et al.  Darboux Transformations and Solitons , 1992 .

[5]  Anjan Biswas,et al.  Optical soliton perturbation in a non-Kerr law media , 2008 .

[6]  T. Davydova,et al.  Schrödinger ordinary solitons and chirped solitons: fourth-order dispersive effects and cubic-quintic nonlinearity , 2001 .

[7]  Bo Tian,et al.  Conservation laws, soliton solutions and modulational instability for the higher-order dispersive nonlinear Schrödinger equation , 2009 .

[8]  Guosheng Zhou,et al.  Properties of soliton solutions on a cw background in optical fibers with higher-order effects , 2004 .

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

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

[11]  P. Becker,et al.  Compression of optical pulses to six femtoseconds by using cubic phase compensation. , 1987, Optics letters.

[12]  S. L. Palacios,et al.  Black optical solitons for media with parabolic nonlinearity law in the presence of fourth order dispersion , 2000 .

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

[14]  Lu Li,et al.  Modulation instability and solitons on a cw background in an optical fiber with higher-order effects. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[16]  M. Ablowitz,et al.  Nonlinear-evolution equations of physical significance , 1973 .

[17]  Guosheng Zhou,et al.  Modulation instability and solitons on a cw background in inhomogeneous optical fiber media , 2004 .

[18]  L. Kavitha,et al.  SOLITON SPIN EXCITATIONS IN AN ANISOTROPIC HEISENBERG FERROMAGNET WITH OCTUPOLE-DIPOLE INTERACTION , 1999 .

[19]  Andrei I. Maimistov,et al.  Unidirectional propagation of an ultra-short electromagnetic pulse in a resonant medium with high frequency Stark shift , 2001, nlin/0107040.

[20]  H. Triki,et al.  Solitary wave solutions for high dispersive cubic-quintic nonlinear Schrödinger equation , 2009 .

[21]  M. Lakshmanan,et al.  On the integrability aspects of the one-dimensional classical continuum isotropic biquadratic Heisenberg spin chain , 1992 .

[22]  Anjan Biswas,et al.  Optical soliton perturbation in non-Kerr law media: Traveling wave solution , 2012 .

[23]  F. Krausz,et al.  Generation of 0.1-TW 5-fs optical pulses at a 1-kHz repetition rate. , 1997, Optics letters.

[24]  Lu Li,et al.  Dark solitons on an intense parabolic background in nonlinear waveguides , 2008 .

[25]  K. Porsezian,et al.  Modulational instability in optical fibers with arbitrary higher-order dispersion and delayed Raman response , 2006 .

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

[27]  Akihisa Tomita,et al.  1100× optical fiber pulse compression using grating pair and soliton effect at 1.319 μm , 1986 .

[28]  A. Kamchatnov,et al.  Nonlinear periodic waves and their modulations , 2000 .

[29]  A. M. Basharov,et al.  Nonlinear Optical Waves , 1999 .

[30]  NONLINEAR OPTICAL PHENOMENA AND DEVICES: Propagation of ultrashort pulses through a nonresonance quadratically nonlinear medium in the unidirectional wave approximation , 2000 .