Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations
type: Item
instance of: scholarly article
title: Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations
zbMATH Open document ID: 1452.37069
author: Wen-Xiu Ma
published in: Journal of Geometry and Physics
publication date: 2020-09-17T00:00:00Z
review text: The paper is devoted to a nonlocal modification of the Korteweg-de Vries equation. The nonlocality of the model manifests in the presence, in the corresponding nonlinear differential equation, of a term depending on inverted space-time coordinates. In addition, the author considers even larger, multicomponent class of mKdV equations. It turns out that such nonlolcal generalization possesses a Lax pair formulation which results in the complete integrability of the model. Then the author applies the inverse scattering method by means of the corresponding Riemann-Hilbert problem, which is one of the equivalent approaches to finding the explicit solutions. The investigation is done along the lines of classical works on the inverse scattering method. The author routinely formulates the related spectral problem, finds the time evolution of the scattering data, and finds the corresponding Gelfand-Levitan-Marchenko integral equations, which encode the soliton solutions. The presentation of the paper is quite complete, and contains many technical details and explicit calculations.
reviewed by: A. Melikyan
Mathematics Subject Classification ID: 37K15
Mathematics Subject Classification ID: 37K40
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q15
zbMATH DE Number: 7248562
zbMATH Keywords: reverse space-time
zbMATH Keywords: nonlocal integrable equation
zbMATH Keywords: matrix spectral problem
zbMATH Keywords: inverse scattering transform
zbMATH Keywords: Riemann-Hilbert problem
zbMATH Keywords: soliton solution
MaRDI profile type: Publication
full work available at URL: j.geomphys.2020.103845
OpenAlex ID: W3047889030
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DOI: 10.1016/J.GEOMPHYS.2020.103845
description: scientific article