4.5 Article

Nonlocal integrable mKdV equations by two nonlocal reductions and their soliton solutions

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

Riemann-Hilbert problems and inverse scattering of nonlocal real reverse-spacetime matrix AKNS hierarchies

Wen-Xiu Ma

Summary: This study proposes a nonlocal real reverse-spacetime integrable hierarchies of PT symmetric matrix AKNS equations, achieved through nonlocal symmetry reductions on the potential matrix, to determine generalized Jost solutions. By applying the Sokhotski-Plemelj formula, the associated Riemann-Hilbert problems are transformed into integral equations of Gelfand-Levitan-Marchenko type. The Riemann-Hilbert problems corresponding to the reflectionless case are explicitly solved, presenting soliton solutions for the resulting nonlocal real reverse-spacetime integrable PT-symmetric matrix AKNS equations.

PHYSICA D-NONLINEAR PHENOMENA (2022)

Article Mathematics

Riemann-Hilbert Problems and Soliton Solutions of Nonlocal Reverse-Time NLS Hierarchies

Wenxiu Ma

Summary: This paper focuses on establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger (NLS) hierarchies associated with higher-order matrix spectral problems. The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix, corresponding to the reflectionless inverse scattering transforms, is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reverse-time NLS hierarchies.

ACTA MATHEMATICA SCIENTIA (2022)

Article Mathematics

Riemann-Hilbert Problems and Soliton Solutions of Type (λ*, -λ*) Reduced Nonlocal Integrable mKdV Hierarchies

Wen-Xiu Ma

Summary: Reduced nonlocal matrix integrable modified Korteweg-de Vries (mKdV) hierarchies are obtained through two transpose-type group reductions in the matrix Ablowitz-Kaup-Newell-Segur (AKNS) spectral problems. Riemann-Hilbert problems and soliton solutions are formulated based on the reduced matrix spectral problems.

MATHEMATICS (2022)

Article Mathematics, Applied

Type (-λ, -λ*) reduced nonlocal integrable mKdV equations and their soliton solutions

Wen-Xiu Ma

Summary: A novel reduced nonlocal integrable mKdV equation of odd order is presented by taking two group reductions of the AKNS matrix spectral problems. Soliton solutions are generated from the corresponding reflectionless Riemann-Hilbert problems based on the distribution of eigenvalues.

APPLIED MATHEMATICS LETTERS (2022)

Article Mathematics, Applied

INVERSE SCATTERING AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-SPACETIME NONLINEAR SCHRODINGER EQUATIONS

Wen-Xiu Ma

Summary: This paper presents nonlocal reverse-spacetime PT-symmetric multicomponent nonlinear Schrodinger equations and their inverse scattering transforms and soliton solutions using the Riemann-Hilbert technique under a specific nonlocal group reduction. The Sokhotski-Plemelj formula is used to determine solutions to a class of associated Riemann-Hilbert problems and transform the systems that generalized Jost solutions need to satisfy. A formulation of solutions is developed for the Riemann-Hilbert problems associated with the reflectionless transforms, and soliton solutions are constructed for the presented nonlocal reverse-spacetime PT-symmetric NLS equations.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2021)

Article Multidisciplinary Sciences

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

Liming Ling et al.

Summary: This paper investigates the soliton solutions of nonlocal complex reverse-spacetime mKdV hierarchies through nonlocal symmetry reductions of matrix spectral problems. By formulating the corresponding inverse scattering problems and constructing solutions to specific Riemann-Hilbert problems, N-soliton solutions to the hierarchies are obtained.

SYMMETRY-BASEL (2021)

Article Mathematics, Applied

Inverse scattering for nonlocal reverse-time nonlinear Schrodinger equations

Wen-Xiu Ma

APPLIED MATHEMATICS LETTERS (2020)

Article Mathematics, Applied

Nonlocal modified KdV equations and their soliton solutions by Hirota Method

Metin Gurses et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2019)

Article Mathematics, Applied

Riemann-Hilbert problems and soliton solutions of a multicomponent mKdV system and its reduction

Wen-Xiu Ma

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2019)

Article Physics, Multidisciplinary

General N-solitons and their dynamics in several nonlocal nonlinear Schrodinger equations

Jianke Yang

PHYSICS LETTERS A (2019)

Article Mathematics

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

Wen-Xiu Ma et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2018)

Article Physics, Mathematical

Nonlocal nonlinear Schrodinger equations and their soliton solutions

Metin Gurses et al.

JOURNAL OF MATHEMATICAL PHYSICS (2018)

Article Mathematics, Applied

Integrable Nonlocal Nonlinear Equations

Mark J. Ablowitz et al.

STUDIES IN APPLIED MATHEMATICS (2017)

Article Mathematics, Applied

Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform

Jia-Liang Ji et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2017)

Article Mathematics, Applied

On a nonlocal modified Korteweg-de Vries equation: Integrability, Darboux transformation and soliton solutions

Jia-Liang Ji et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2017)

Article Mathematics, Applied

Solitons and dynamics for a general integrable nonlocal coupled nonlinear Schrodinger equation

Cai-Qin Song et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2017)

Article Mathematics

A Riemann-Hilbert Approach to the Harry-Dym Equation on the Line

Yu Xiao et al.

CHINESE ANNALS OF MATHEMATICS SERIES B (2016)

Article Mathematics, Applied

Inverse scattering transform for the integrable nonlocal nonlinear Schrodinger equation

Mark J. Ablowitz et al.

NONLINEARITY (2016)

Article Physics, Mathematical

Integrable properties of the general coupled nonlinear Schrodinger equations

Deng-Shan Wang et al.

JOURNAL OF MATHEMATICAL PHYSICS (2010)