Extension of the module of invertible transformations. Classification of integrable systems
type: Item
instance of: scholarly article
title: Extension of the module of invertible transformations. Classification of integrable systems
zbMATH Open document ID: 0659.35091
DOI: 10.1007/BF01238850
author: A. V. Mikhajlov
author: A. B. Shabat
author: Ravil I. Yamilov
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: We demonstrate that for the systems of equations, which are invariant under a point group or possess conservation laws of the zeroth or first order, a nontrivial extension of the module of invertible transformations is possible. That simplifies greatly a classification of the integrable systems of equations. Here we present an exhaustive list and a classification of the second order systems of the form \[ u_ t=u_{xx}+f(u,v,u_ x,v_ x),\quad -v_ t=v_{xx}+g(u,v,u_ x,v_ x), \] which possess the conservation laws of higher order. The reduction group approach allows us to define the Lax type representations for some new equations of our list.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 4077885
zbMATH Keywords: invariant under a point group
zbMATH Keywords: conservation laws
zbMATH Keywords: invertible transformations
zbMATH Keywords: integrable systems
zbMATH Keywords: second order systems
zbMATH Keywords: Lax type representations
Wikidata QID: Q61835430
MaRDI profile type: Publication
cites work: (L,A)-pairs and a Riccati type substitution
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description: scientific article; zbMATH DE number 4077885