A new conservation theorem

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Nail H. Ibragimov
Title: A new conservation theorem
Journal: Journal of Mathematical Analysis and Applications
Year: 2007
Volume: 333
Issue: 1
Pagination: 311-328
ISSN: 0022-247X
Publisher: Academic Press
ISI number: 000247325900022
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap)
School of Engineering S- 371 79 Karlskrona
+46 455 38 50 00
Authors e-mail: nib@bth.se
Language: English
Abstract: A general theorem on conservation laws for arbitrary differential equations is proved. The theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables. The new theorem does not require existence of a Lagrangian and is based on a concept of an adjoint equation for non-linear equations suggested recently by the author. It is proved that the adjoint equation inherits all symmetries of the original equation. Accordingly, one can associate a conservation law with any group of Lie, Lie-Backlund or non-local symmetries and find conservation laws for differential equations without classical Lagrangians.
Subject: Mathematics\General
Keywords: conservation laws