\(N\)-fold Darboux transformation and double-Wronskian-typed solitonic structures for a variable-coefficient modified Kortweg-de Vries equation
type: Item
instance of: scholarly article
title: \(N\)-fold Darboux transformation and double-Wronskian-typed solitonic structures for a variable-coefficient modified Kortweg-de Vries equation
zbMATH Open document ID: 1268.37085
author: Lei Wang
author: Yi-Tian Gao
author: Feng-Hua Qi
published in: Annals of Physics
publication date: 2012-11-09T00:00:00Z
review text: This paper considers a variable-coefficient modified Korteweg-de Vries equation which appears in certain situations in fluids and plasmas. An \(N\)-fold Darboux transformation of a variable-coefficient Ablowitz-Kaup-Newell-Segur spectral problem is constructed via a gauge transformation. The reduction of this \(N\)-fold Darboux transformation provides multisoliton solutions for this variable-coefficient modified Korteweg-de Vries equation in terms of the double Wronskian determinant. Two- and three-soliton solutions are investigated through graphical representations and three different types of solitonic interactions are discussed: head-on and overtaking collisions and parallel solitons. It is explained how nonlinear, dispersive and dissipative terms affect the velocities of the solitons whilst the amplitudes of the waves depend on the perturbation term.
Mathematics Subject Classification ID: 37K35
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 6104581
zbMATH Keywords: variable-coefficient modified Korteweg-de Vries model
zbMATH Keywords: multi-solitonic solutions
zbMATH Keywords: double Wronskian solution
zbMATH Keywords: \(N\)-fold Darboux transformation
MaRDI profile type: Publication
full work available at URL: j.aop.2012.04.009
OpenAlex ID: W2052406102
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DOI: 10.1016/J.AOP.2012.04.009
description: scientific article; zbMATH DE number 6104581