Inverse scattering transforms for non-local reverse-space matrix non-linear Schrödinger equations

The aim of the paper is to explore non-local reverse-space matrix non-linear Schrödinger equations and their inverse scattering transforms. Riemann–Hilbert problems are formulated to analyse the inverse scattering problems, and the Sokhotski–Plemelj formula is used to determine Gelfand–Levitan–Marchenko-type integral equations for generalised matrix Jost solutions. Soliton solutions are constructed through the reflectionless transforms associated with poles of the Riemann–Hilbert problems.

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Inverse scattering for nonlocal reverse-space multicomponent nonlinear Schrödinger equations

International Journal of Modern Physics B ◽

10.1142/s021797922150051x ◽

2021 ◽

Vol 35 (04) ◽

pp. 2150051

Author(s):

Wen-Xiu Ma ◽

Yehui Huang ◽

Fudong Wang

Keyword(s):

Inverse Scattering ◽

Soliton Solutions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Scattering Problems ◽

Nonlinear Schrödinger ◽

Plemelj Formula ◽

Nonlinear Schrodinger Equations ◽

Generalized Matrix

The paper aims to discuss nonlocal reverse-space multicomponent nonlinear Schrödinger equations and their inverse scattering transforms. The inverse scattering problems are analyzed by means of Riemann–Hilbert problems, and Gelfand–Levitan–Marchenko-type integral equations for generalized matrix Jost solutions are determined by the Sokhotski–Plemelj formula. Soliton solutions are generated from the reflectionless transforms associated with zeros of the Riemann–Hilbert problems.

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Time-dependent method for non-linear Schrödinger equations in inverse scattering problems

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2017.11.012 ◽

2018 ◽

Vol 459 (2) ◽

pp. 932-944 ◽

Cited By ~ 2

Author(s):

Michiyuki Watanabe

Keyword(s):

Inverse Scattering ◽

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Scattering Problems ◽

Inverse Scattering Problems ◽

Non Linear

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The initial value problem, scattering and inverse scattering, for Schrödinger equations with a potential and a non-local nonlinearity

Journal of Physics A General Physics ◽

10.1088/0305-4470/39/37/009 ◽

2006 ◽

Vol 39 (37) ◽

pp. 11461-11478 ◽

Cited By ~ 3

Author(s):

María de los Ángeles Sand Romero ◽

Ricardo Weder

Keyword(s):

Inverse Scattering ◽

Initial Value Problem ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Initial Value ◽

Non Local ◽

Local Nonlinearity

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Inverse scattering and soliton solutions of nonlocal reverse-spacetime nonlinear Schrödinger equations

Proceedings of the American Mathematical Society ◽

10.1090/proc/15174 ◽

2020 ◽

Vol 149 (1) ◽

pp. 251-263

Author(s):

Wen-Xiu Ma

Keyword(s):

Inverse Scattering ◽

Soliton Solutions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Inverse Scattering and Soliton Solutions of Nonlocal Complex Reverse-Spacetime Modified Korteweg-de Vries Hierarchies

Symmetry ◽

10.3390/sym13030512 ◽

2021 ◽

Vol 13 (3) ◽

pp. 512

Author(s):

Liming Ling ◽

Wen-Xiu Ma

Keyword(s):

Inverse Scattering ◽

Soliton Solutions ◽

Identity Matrix ◽

Nonlocal Symmetry ◽

Scattering Problems ◽

Spectral Problems ◽

Symmetry Reductions ◽

Jump Matrix ◽

De Vries ◽

Scattering Transforms

This paper aims to explore nonlocal complex reverse-spacetime modified Korteweg-de Vries (mKdV) hierarchies via nonlocal symmetry reductions of matrix spectral problems and to construct their soliton solutions by the inverse scattering transforms. The corresponding inverse scattering problems are formulated by building the associated Riemann-Hilbert problems. A formulation of solutions to specific Riemann-Hilbert problems, with the jump matrix being the identity matrix, is established, where eigenvalues could equal adjoint eigenvalues, and thus N-soliton solutions to the nonlocal complex reverse-spacetime mKdV hierarchies are obtained from the reflectionless transforms.

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