On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations
type: Item
instance of: scholarly article
title: On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations
zbMATH Open document ID: 1005.37043
DOI: 10.1016/S0960-0779(01)00096-0
author: F. Lambert
author: Johan Springael
published in: Chaos, Solitons and Fractals
publication date: 2002-06-13T00:00:00Z
review text: The authors present a direct and unifying scheme for the disclosure of bilinear Bäcklund transformations and linear Lax systems associated with the soliton equation. The scheme is based on a concept of scale invariance and on the use of a class of partitional polynomials: the binary Bell polynomials. In order to provide a complete picture of the method they start their discussions with the case of NLPDEs which can be derived from a quadratic Hirota equation, considering two simple examples: the KdV equation and the Sawada-Kotera equation.
Mathematics Subject Classification ID: 37K35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1755370
zbMATH Keywords: Hirota equation
zbMATH Keywords: sine-Gordon equation
zbMATH Keywords: modified KdV equation
zbMATH Keywords: coupled ANS system
zbMATH Keywords: bilinear Bäcklund transformations
zbMATH Keywords: linear Lax systems
zbMATH Keywords: soliton equation
zbMATH Keywords: binary Bell polynomials
zbMATH Keywords: KdV equation
zbMATH Keywords: Sawada-Kotera equation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Bäcklund transformations, the inverse scattering method, solitons, and their applications. NSF research workshop on contact transformations
cites work: A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem
cites work: Construction of Bäcklund Transformations with Binary Bell Polynomials
cites work: On the combinatorics of the HirotaD-operators
cites work: Exponential polynomials
cites work: A Bäcklund transformation for a higher order Korteweg-de Vries equation
cites work: Nonlinear-evolution equations of physical significance
full work available at URL: s0960-0779(01)00096-0
OpenAlex ID: W2033780749
description: scientific article; zbMATH DE number 1755370