Discrete symmetries and solitons
type: Item
instance of: scholarly article
title: Discrete symmetries and solitons
zbMATH Open document ID: 0860.35111
DOI: 10.1007/BF01017068
published in: Theoretical and Mathematical Physics
publication date: 1996-09-03T00:00:00Z
review text: The paper discusses the relation between the discrete symmetries associated with some nonlinear evolution equations and the corresponding spectral problems. In particular, it shows the connection between the Schrödinger equation \(L\psi= -\psi'' + u(x) \psi = \lambda \psi\) and the nonlinear lattice equations \[ (f_n+f_{n+1})' =f^2_n-f^2_{n+1} + \alpha_n, \] where \(n=0\), \(\pm 1, \dots\) and \(\alpha_n\) are constants. It is also shown how Bäcklund transformations and \(N\)-soliton solutions can be obtained directly from the symmetries.
reviewed by: Yuri S. Kivshar
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 907340
zbMATH Keywords: \(N\)-soliton solutions
zbMATH Keywords: discrete symmetries
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: lattice equations
zbMATH Keywords: Bäcklund transformations
author: A. B. Shabat
MaRDI profile type: Publication
cites work: Q4090743
cites work: A correction to the paper ``Hypergeometric functions and toric varieties''
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cites work: Q3209477
cites work: Periodic fixed points of Bäcklund transformations and the Korteweg–de Vries equation
cites work: The Factorization Method
cites work: Construction of reflectionless potentials with infinite discrete spectrum
full work available at URL: https://doi.org/10.1007/bf01017068
OpenAlex ID: W2048651940
description: scientific article; zbMATH DE number 907340