A new conservation theorem
type: Item
instance of: scholarly article
title: A new conservation theorem
zbMATH Open document ID: 1160.35008
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-06-26T00:00:00Z
review text: A classical result in the calculus of variations is the Noether theorem that every variational symmetry has an associated conservation law. The author proposes an extension of this result to arbitrary differential equations not necessarily of a variational nature. It is based on a novel concept of adjoint for nonlinear equations. The author shows first that the system consisting of the original equation plus its adjoint is variational and then that every symmetry of the original equation can be extended to one of the combined system. Now a straightforward application of the classical Noether theorem yields a conservation law. As the definition of a nonlinear adjoint requires the introduction of additional unknown functions, one obtains in general even an infinite familiy of conservation laws parametrised by solutions of the adjoint equation. As concrete examples the heat and the Korteweg-de Vries equations are studied.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 5167519
zbMATH Keywords: nonlinear adjoint
zbMATH Keywords: Lagrangian
zbMATH Keywords: conservation law
zbMATH Keywords: Noether theorem
author: Nail H. Ibragimov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.10.078
OpenAlex ID: W2085413857
cites work: Q3223508
cites work: Q4357207
cites work: Integrating factors, adjoint equations and Lagrangians
cites work: Q3857211
DOI: 10.1016/J.JMAA.2006.10.078
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description: scientific article; zbMATH DE number 5167519