Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov–Ivanov equation under the zero/nonzero background

[1]  Yongshuai Zhang,et al.  The regularity of the multiple higher‐order poles solitons of the NLS equation , 2020, Studies in Applied Mathematics.

[2]  E. Fan,et al.  Inverse scattering transform for the Gerdjikov–Ivanov equation with nonzero boundary conditions , 2020, Zeitschrift für angewandte Mathematik und Physik.

[3]  Yongshuai Zhang,et al.  The bound-state soliton solutions of the complex modified KdV equation , 2020, Inverse Problems.

[4]  J. Rao,et al.  Riemann–Hilbert method for the Wadati–Konno–Ichikawa equation: N simple poles and one higher-order pole , 2019 .

[5]  Xianguo Geng,et al.  Trace formula and new form of N-soliton to the Gerdjikov–Ivanov equation , 2018 .

[6]  Robert Buckingham,et al.  Large-Order Asymptotics for Multiple-Pole Solitons of the Focusing Nonlinear Schrödinger Equation , 2018, Journal of Nonlinear Science.

[7]  G. Biondini,et al.  On the focusing non-linear Schrödinger equation with non-zero boundary conditions and double poles , 2017 .

[8]  Gino Biondini,et al.  The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions , 2015, 1511.02885.

[9]  Gino Biondini,et al.  Inverse Scattering Transform for the Defocusing Manakov System with Nonzero Boundary Conditions , 2015, SIAM J. Math. Anal..

[10]  Gino Biondini,et al.  Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions , 2014 .

[11]  Engui Fan,et al.  Algebro-geometric solutions for the Gerdjikov-Ivanov hierarchy , 2013 .

[12]  Federica Vitale,et al.  The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions , 2013 .

[13]  Jianke Yang,et al.  Nonlinear Waves in Integrable and Nonintegrable Systems , 2010, Mathematical modeling and computation.

[14]  Bin He,et al.  Bifurcations and new exact travelling wave solutions for the Gerdjikov–Ivanov equation , 2010 .

[15]  Gino Biondini,et al.  Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions , 2006 .

[16]  Saburo Kakei,et al.  SOLUTIONS OF A DERIVATIVE NONLINEAR SCHRÖDINGER HIERARCHY AND ITS SIMILARITY REDUCTION , 2005, Glasgow Mathematical Journal.

[17]  Engui Fan,et al.  Variable separation and algebro-geometric solutions of the Gerdjikov–Ivanov equation , 2004 .

[18]  E. Fan,et al.  A family of completely integrable multi-Hamiltonian systems explicitly related to some celebrated equations , 2001 .

[19]  Engui Fan,et al.  Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation , 2000 .

[20]  J. Satsuma,et al.  Bilinearization of a Generalized Derivative Nonlinear Schrödinger Equation , 1995, solv-int/9501005.

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

[22]  P. Deift,et al.  A steepest descent method for oscillatory Riemann-Hilbert problems , 1992, math/9201261.

[23]  E. Mjølhus.  Nonlinear Alfvén waves and the DNLS equation: oblique aspects , 1989 .

[24]  A. Hasegawa,et al.  Fission of optical solitons induced by stimulated Raman effect. , 1988, Optics letters.

[25]  A. Hasegawa,et al.  Nonlinear pulse propagation in a monomode dielectric guide , 1987 .

[26]  A. Kundu.  Exact solutions to higher-order nonlinear equations through gauge transformation , 1987 .

[27]  Yuji Kodama,et al.  Optical solitons in a monomode fiber , 1985 .

[28]  M. Wadati,et al.  The Multiple Pole Solutions of the Sine-Gordon Equation , 1984 .

[29]  Kenji Ohkuma,et al.  Multiple-Pole Solutions of the Modified Korteweg-de Vries Equation , 1982 .

[30]  Daniel R. Grischkowsky,et al.  Nonlinear Picosecond-Pulse Propagation Through Optical Fibers with Positive Group Velocity Dispersion , 1981 .

[31]  Narkis Tzoar,et al.  Self-phase modulation in long-geometry optical waveguides , 1981 .

[32]  H. H. Chen,et al.  Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method , 1979 .

[33]  David J. Kaup,et al.  An exact solution for a derivative nonlinear Schrödinger equation , 1978 .

[34]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

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

[36]  Mark J. Ablowitz,et al.  Multidimensional nonlinear evolution equations and inverse scattering , 1986 .

[37]  A. Rogister.  Parallel Propagation of Nonlinear Low‐Frequency Waves in High‐β Plasma , 1971 .

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