Bäcklund transformation and exact soliton solutions for some nonlinear evolution equations of the ZS/AKNS system
type: Item
instance of: scholarly article
title: Bäcklund transformation and exact soliton solutions for some nonlinear evolution equations of the ZS/AKNS system
zbMATH Open document ID: 0933.37068
DOI: 10.1016/S0960-0779(97)00186-0
author: A. H. Khater
author: R. S. Ibrahim
author: D. K. Callebaut
author: O. H. EL-Kalaawy
published in: Chaos, Solitons and Fractals
publication date: 2000-04-09T00:00:00Z
review text: The Bäcklund transformations (BTs) technique is one of the direct methods to obtain the new soliton solutions of a given nonlinear evolution equations (NLEEs). The Bäcklund transformations explicitly express the new solutions in terms of the known solutions of the NLEEs and the corresponding wave functions which are solutions of the associated Zakharov-Shabat/Ablowitz-Kaup-Newell-Segur (ZS/AKNS) system. The main goal of this paper is to use BTs in the construction of exact soliton solutions for some classes of NLEEs, for instance: for KdV, mKdV, Liouville, stable and nonstable Schrödinger and many others. To this end the method of characteristics is used.
Mathematics Subject Classification ID: 37K40
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 37K35
zbMATH DE Number: 1371614
zbMATH Keywords: ZS/AKNS systems
zbMATH Keywords: Bäcklund transformations
zbMATH Keywords: exact soliton solutions
zbMATH Keywords: KdV
zbMATH Keywords: mKdV
zbMATH Keywords: method of characteristic
zbMATH Keywords: Liouville
zbMATH Keywords: nonstable Schrödinger
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q3995225
cites work: Bäcklund transformations: exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations
cites work: Bäcklund transformations and their applications
full work available at URL: s0960-0779(97)00186-0
OpenAlex ID: W1494311747
description: scientific article; zbMATH DE number 1371614