Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations

Ma Wen-Xiu

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Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations

机译：非本体复合反向 - 时空MKDV方程的逆散射和孤子解

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The paper deals with the inverse scattering transforms for nonlocal complex reverse-spacetime multicomponent integrable modified Korteweg-de Vries (mKdV) equations. We establish associated Riemann-Hilbert problems and determine their solutions by the Sokhotski-Plemelj formula. The inverse scattering problems consist of Gelfand-Levitan-Marchenko type equations for the generalized matrix Jost solutions and the recovery formula for the potential. When reflection coefficients are zero, the corresponding Riemann-Hilbert problems yield soliton solutions to the nonlocal complex reverse-spacetime mKdV equations. (C) 2020 Elsevier B.V. All rights reserved.

机译：本文涉及非局部复杂反向时空的逆散射变换，多组分可集成的korteweg-de VRIES（MKDV）方程。我们建立了相关的riemann-hilbert问题，并通过Sokhotski-Plemelj公式确定其解决方案。逆散射问题由Gelfand-Levitan-Marchenko类型方程组成，用于广义矩阵Jost解决方案和潜在恢复公式。当反射系数为零时，相应的RIEMANN-HILBERT问题将孤子解决方案产生孤子解决方案。（c）2020 Elsevier B.V.保留所有权利。

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来源
《Journal of geometry and physics》 |2020年第1期|共8页
作者
Ma Wen-Xiu;
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作者单位

South China Univ Technol Sch Math Guangzhou 510640 Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类数学物理方法;几何、拓扑;
关键词
Reverse-spacetime nonlocal integrable equation; Matrix spectral problem; Inverse scattering transform; Riemann-Hilbert problem; Soliton solution;

机译：反向时空非局部完全方程;矩阵光谱问题;逆散射变换;riemann-hilbert问题;孤子解决方案;

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1. Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations [J] . Ma Wen-Xiu Journal of geometry and physics . 2020,第1期

机译：非本体复合反向 - 时空MKDV方程的逆散射和孤子解
2. Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions [J] . Physica, D. Nonlinear phenomena . 2020,第期

机译：具有非零边界条件的聚焦和散焦的逆散射变换和孤子解决方案
3. Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions [J] . Zhang Guoqiang, Yan Zhenya Physica, D. Nonlinear phenomena . 2020,第期

机译：具有非零边界条件的聚焦和散焦MKDV方程：逆散射变换和孤子交互
4. Verifying the Soliton Solutions to the Fifth Order KdV Equation by Ordinary Inverse Scattering Method [C] . Chao Ma, Jin-chun He International Conference on Green Materials and Environmental Engineering . 2014

机译：普通逆散射法将孤子解决方案验证到第五阶KDV方程
5. Soliton solutions of nonlinear partial differential equations using variational approximations and inverse scattering techniques. [D] . Vogel, Thomas K. 2007

机译：使用变分近似和逆散射技术的非线性偏微分方程的孤子解。
6. Bright-Dark and Multi Solitons Solutions of (3 + 1)-Dimensional Cubic-Quintic Complex Ginzburg–Landau Dynamical Equation with Applications and Stability [O] . Chen Yue, Dianchen Lu, Muhammad Arshad, 2020

机译：（3 + 1） - 二维立方 - Quid-Complex Ginzburg-Landau的亮度和多孤子解决方案具有应用和稳定性的动态方程
7. Inverse Scattering and Soliton Solutions of Nonlocal Complex Reverse-Spacetime Modified Korteweg-de Vries Hierarchies [O] . Liming Ling, Wen-Xiu Ma 2021

机译：非识别复合反向时空的逆散射和孤子解决方案修改了Korteweg-de Vries层次结构
8. Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation. [R] . Arkadiev, V. A., Pogrebkov, A. K., Polivanov, M. C. 1989

机译：Davey-stewartson II方程的逆散射变换方法和孤子解。

Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations

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