The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions
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[1] S K Turitsyn,et al. Vector dark solitons. , 1993, Optics letters.
[2] Frédéric Dias,et al. The Peregrine soliton in nonlinear fibre optics , 2010 .
[3] M. Lakshmanan,et al. Bright and dark soliton solutions to coupled nonlinear Schrodinger equations , 1995 .
[4] Li-Chen Zhao,et al. Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.
[5] Gino Biondini,et al. Elastic and inelastic line-soliton solutions of the Kadomtsev-Petviashvili II equation , 2005, Math. Comput. Simul..
[6] P. Deift,et al. The collisionless shock region for the long-time behavior of solutions of the KdV equation , 1994 .
[7] A. Vartanian. Long-Time Asymptotics of Solutions to the Cauchy Problem for the Defocusing Non-Linear Schr\"{o}dinger Equation with Finite Density Initial Data. I. Solitonless Sector , 2001, nlin/0110024.
[8] 和達 三樹. M. J. Ablowitz and H. Segur: Solitons and the Inverse Scattering Transform, Society for Industrial and Applied Mathematics, Philadelphia, 1981, x+425ページ, 23.5×16.5cm, $54.40 (SIAM Studies in Applied Mathematics). , 1982 .
[9] C. Mee,et al. The inverse scattering transform for the focusing nonlinear Schrödinger equation with asymmetric boundary conditions , 2014 .
[10] M. Boiti,et al. The spectral transform for the NLS equation with left-right asymmetric boundary conditions , 1982 .
[11] Yuji Kodama,et al. Young diagrams and N-soliton solutions of the KP equation , 2004, nlin/0406033.
[12] Federica Vitale,et al. The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions , 2013 .
[13] Richard Squier,et al. Collisions of two solitons in an arbitrary number of coupled nonlinear Schrödinger equations. , 2003, Physical review letters.
[14] Gino Biondini,et al. The Integrable Nature of Modulational Instability , 2015, SIAM J. Appl. Math..
[15] C. Hamner,et al. Generation of dark-bright soliton trains in superfluid-superfluid counterflow. , 2010, Physical review letters.
[16] P. Drazin. SOLITONS, NONLINEAR EVOLUTION EQUATIONS AND INVERSE SCATTERING (London Mathematical Society Lecture Note Series 149) , 1993 .
[17] Yuji Kodama,et al. The Deodhar decomposition of the Grassmannian and the regularity of KP solitons , 2012, 1204.6446.
[18] D. J. Kaup,et al. The Three-Wave Interaction-A Nondispersive Phenomenon , 1976 .
[19] P. Deift,et al. Inverse scattering on the line , 1979 .
[20] A. Vartanian,et al. Long-Time Asymptotics of Solutions to the Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with Finite-Density Initial Data. II. Dark Solitons on Continua , 2002 .
[21] C. Hamner,et al. Dark-dark solitons and modulational instability in miscible two-component Bose-Einstein condensates , 2010, 1007.4947.
[22] T. Frankel. The geometry of physics : an introduction , 2004 .
[23] P. Deift,et al. A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation , 1992, math/9201261.
[24] Yuri S. Kivshar,et al. Polarized dark solitons in isotropic Kerr media , 1997 .
[25] Y. Kodama,et al. KP solitons, total positivity, and cluster algebras , 2011, Proceedings of the National Academy of Sciences.
[26] David W. Lewis,et al. Matrix theory , 1991 .
[27] Leon A. Takhtajan,et al. Hamiltonian methods in the theory of solitons , 1987 .
[28] R. Dodd,et al. Review: L. D. Faddeev and L. A. Takhtajan, Hamiltonian methods in the theory of solitons , 1988 .
[29] Gino Biondini,et al. Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions , 2014 .
[30] William E. Schiesser,et al. Linear and nonlinear waves , 2009, Scholarpedia.
[31] B. Prinari,et al. Dark–dark and dark–bright soliton interactions in the two-component defocusing nonlinear Schrödinger equation , 2013 .
[32] K. Steiglitz,et al. Energy-Exchange Interactions between Colliding Vector Solitons , 1999 .
[33] G. Kovačič,et al. The focusing Manakov system with nonzero boundary conditions , 2015 .
[34] P. G. Kevrekidis,et al. Beating dark–dark solitons in Bose–Einstein condensates , 2012, 1202.2777.
[35] Gino Biondini,et al. On a family of solutions of the Kadomtsev–Petviashvili equation which also satisfy the Toda lattice hierarchy , 2003, nlin/0306003.
[36] P. Deift,et al. A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation , 1993 .
[37] Helge Holden,et al. Soliton Equations and Their Algebro-Geometric Solutions: The AKNS Hierarchy , 2003 .
[38] S. Novikov,et al. Theory of Solitons: The Inverse Scattering Method , 1984 .
[39] Y. Kodama,et al. Submitted to: J. Phys. A: Math. Gen. , 2003 .
[40] M. Ablowitz,et al. Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .
[41] Gino Biondini,et al. Inverse Scattering Transform for the Defocusing Manakov System with Nonzero Boundary Conditions , 2015, SIAM J. Math. Anal..
[42] Gino Biondini,et al. Inverse Scattering Transform for the Multi‐Component Nonlinear Schrödinger Equation with Nonzero Boundary Conditions , 2011 .
[43] L. Chambers. Linear and Nonlinear Waves , 2000, The Mathematical Gazette.
[44] C. S. Gardner,et al. Method for solving the Korteweg-deVries equation , 1967 .
[45] Ronald R. Coifman,et al. Scattering and inverse scattering for first order systems , 1984 .
[46] R. Sachs. Review: Richard Beals, Percy Deift and Carlos Tomei, Direct and inverse scattering on the line , 1990 .
[47] M. Ablowitz,et al. Soliton interactions in the vector NLS equation , 2004 .
[48] D. Mihalache,et al. Multichannel soliton transmission and pulse shepherding in bit-parallel-wavelength optical fiber links , 2002 .
[49] Mark J. Ablowitz,et al. Solitons and the Inverse Scattering Transform , 1981 .
[50] B. Prinari,et al. The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions , 2015, Communications in Mathematical Physics.
[52] Xin Zhou,et al. Direct and inverse scattering transforms with arbitrary spectral singularities , 1989 .
[53] Gino Biondini,et al. On the Spectrum of the Dirac Operator and the Existence of Discrete Eigenvalues for the Defocusing Nonlinear Schrödinger Equation , 2014 .
[54] A. Ustinov. Asymptotic solution of the Cauchy problem for the nonlinear Schrödinger equation with boundary conditions of finite density type , 1989 .
[55] A. Vartanian,et al. Exponentially small asymptotics of solutions to the defocusing nonlinear Schrödinger equation: II , 2001 .
[56] A. B. Shabat,et al. Interaction between solitons in a stable medium , 1973 .
[57] Gino Biondini,et al. Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions , 2006 .
[58] P. Lax. INTEGRALS OF NONLINEAR EQUATIONS OF EVOLUTION AND SOLITARY WAVES. , 1968 .
[59] C. Sulem,et al. The nonlinear Schrödinger equation : self-focusing and wave collapse , 2004 .
[60] Q. Park,et al. Systematic construction of multicomponent optical solitons , 2000 .
[61] J. R. Ensher,et al. Dynamics of component separation in a binary mixture of Bose-Einstein condensates , 1998 .
[62] Gino Biondini,et al. Soliton solutions of the Kadomtsev-Petviashvili II equation , 2006 .
[63] K. Nakkeeran,et al. Exact dark soliton solutions for a family of N coupled nonlinear Schrödinger equations in optical fiber media. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.
[64] G. B. Whitham,et al. Linear and Nonlinear Waves: Whitham/Linear , 1999 .
[65] Gino Biondini,et al. Line soliton interactions of the Kadomtsev-Petviashvili equation. , 2007, Physical review letters.
[66] G. Rowlands,et al. Nonlinear Waves, Solitons and Chaos , 1990 .
[67] E. Belokolos,et al. Algebro-geometric approach to nonlinear integrable equations , 1994 .
[68] A.H. Vartanian,et al. Exponentially small asymptotics of solutions to the defocusing nonlinear Schrödinger equation , 2003, Appl. Math. Lett..
[69] B. Prinari,et al. Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions , 2016 .
[70] S. V. Manakov. On the theory of two-dimensional stationary self-focusing of electromagnetic waves , 1973 .
[71] Kenneth Steiglitz,et al. State transformations of colliding optical solitons and possible application to computation in bulk media , 1998 .
[72] Helge Holden,et al. Soliton Equations and Their Algebro-Geometric Solutions: Bibliography , 2003 .
[73] Carlos Tomei,et al. Direct and inverse scattering on the line , 1988 .
[74] Yasuhiro Ohta,et al. General N‐Dark–Dark Solitons in the Coupled Nonlinear Schrödinger Equations , 2011 .
[75] Yuji Kodama,et al. Classification of the line-soliton solutions of KPII , 2007, 0710.1456.
[76] L. Ostrovsky,et al. Modulation instability: The beginning , 2009 .
[77] Pelinovsky,et al. Stability criterion for multicomponent solitary waves , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[78] V. Zakharov,et al. Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media , 1970 .
[79] B. Prinari,et al. Polarization interactions in multi-component defocusing media , 2015 .
[80] Fabio Baronio,et al. Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves. , 2012, Physical review letters.
[81] K. Bongs,et al. Oscillations and interactions of dark and dark bright solitons in Bose Einstein condensates , 2008 .