On the integrability of systems of second order evolution equations with two components
type: Item
instance of: scholarly article
title: On the integrability of systems of second order evolution equations with two components
zbMATH Open document ID: 1061.35036
author: Jing Ping Wang
author: Jan A. Sanders
published in: Journal of Differential Equations
publication date: 2004-08-20T00:00:00Z
review text: The paper aims to develop a symmetry classification of coupled systems of two nonlinear partial differential equations of the parabolic type (with two independent variables) with nonzero linear diagonal elements and nonlinearity represented by homogeneous polynomials. The eventual objective is to identify systems that are integrable in the sense of having an infinite number of symmetries. The analysis is based on computer-assisted symbolic calulations (running in Maple) that aim to find coefficient sets that support the existence of infinite series of the symmetries. The completeness of the classification is proven. The integrable systems found in the work are cast in a form without quadratic nonlinear terms, but with cubic ones necessarily present. The paper ends with giving lists of the integrable systems, and comparison with earlier works, where some of those systems have already been found.
reviewed by: B. A. Malomed
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 2093535
zbMATH Keywords: symbolic methods
zbMATH Keywords: symmetry-integrability
zbMATH Keywords: Lech-Mahler theorem
zbMATH Keywords: implict function theorem
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: j.jde.2004.04.010
OpenAlex ID: W2034870255
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DOI: 10.1016/J.JDE.2004.04.010
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description: scientific article; zbMATH DE number 2093535