Recursion and group structures of soliton equations
type: Item
instance of: scholarly article
title: Recursion and group structures of soliton equations
zbMATH Open document ID: 0678.58019
DOI: 10.1007/BF00046887
published in: Acta Applicandae Mathematicae
publication date: 1989-01-01T00:00:00Z
review text: This survey article discusses integrable equations in \(1+1\) and \(1+2\) dimensions. Starting with a spectral problem, the recursion operator and the group of Bäcklund transformations are constructed. It is shown how one finds the integrable equations back from it. Special-type Bäcklund transformations are constructed for several examples.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4111636
zbMATH Keywords: recursion operator
zbMATH Keywords: integrable equation
zbMATH Keywords: Bäcklund transformations
author: B. Konopelchenko
MaRDI profile type: Publication
cites work: Method for Solving the Korteweg-deVries Equation
cites work: Q3732104
cites work: Q3889412
cites work: Q3925229
cites work: Solitons. Mathematical methods for physicists
cites work: Q3966539
cites work: Q3961178
cites work: Q3679549
cites work: Q3893000
cites work: Q3311238
cites work: Q3721001
cites work: Bäcklund transformations, the inverse scattering method, solitons, and their applications. NSF research workshop on contact transformations
cites work: Bäcklund transformations and their applications
cites work: Korteweg‐devries equation and generalizations. VI. methods for exact solution
cites work: Conservation laws for classes of nonlinear evolution equations solvable by the spectral transform
cites work: A simple model of the integrable Hamiltonian equation
cites work: Nonlinear integrable equations. Recursion operators, group-theoretical and Hamiltonian structures of soliton equations
cites work: Recursion and group structures of the integrable equations in 1+1 and 1+2 dimensions. Bilocal approach
cites work: Nonformal recursion operators and nonlinear integrable evolution equations
cites work: Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
cites work: Bäcklund transformations connecting different isospectral deformation equations
cites work: Closure of the squared Zakharov-Shabat eigenstates
cites work: The general structure of integrable evolution equations
cites work: On the structure of equations integrable by the arbitrary-order linear spectral problem
cites work: Backlund transformations via gauge transformations in 2+1 dimensions
full work available at URL: https://doi.org/10.1007/bf00046887
OpenAlex ID: W4241107186
description: scientific article; zbMATH DE number 4111636