Nonlinear self-adjointness and conservation laws

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Nail H. Ibragimov
Title: Nonlinear self-adjointness and conservation laws
Journal: Journal of Physics A: Mathematical and Theoretical
Year: 2011
Volume: 44
Issue: 43
Pagination: Article number 432002
ISSN: 1751-8113
Publisher: IOP Science
URI/DOI: 10.1088/1751-8113/44/43/432002
ISI number: 000296147000002
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
Language: English
Abstract: The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation ut u = 0 becomes strictly self-adjoint after multiplying by u1. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems.
Subject: Mathematics\General