Riemann-Hilbert problems and soliton solutions of nonlocal real reverse-spacetime mKdV equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:498

Article

Ma, Wen-Xiu^1,2,3,4 

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[2] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

[3] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA

[4] North West Univ, Sch Math & Stat Sci, Mafikeng Campus,Private Bag X2046, ZA-2735 Mmabatho, South Africa

关键词: Matrix spectral problem;    Nonlocal reverse-spacetime integrable equation;    Riemann-Hilbert problem;    Inverse scattering transform;    Soliton solution;    Parity-time symmetry;   

DOI  :  10.1016/j.jmaa.2021.124980

来源: Elsevier

【 摘 要 】

We would like to analyze a kind of nonlocal reverse-spacetime integrable PT-symmetric multicomponent modified Korteweg-de Vires (mKdV) equations by making a group of nonlocal reductions, and establish their associated Riemann-Hilbert problems which determine generalized Jost solutions of higher-order matrix spectral problems. The Sokhotski-Plemelj formula is used to transform the associated Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. The Riemann-Hilbert problems in the reflectionless case are solved explicitly, and the resulting formulation of solutions enables us to present solitons to the nonlocal reverse-spacetime integrable PT-symmetric mKdV equations. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free