Lagrangian approach to evolution equations: symmetries and conservation laws.

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Nail H. Ibragimov, T. Kolsrud
Title: Lagrangian approach to evolution equations: symmetries and conservation laws.
Translated title: Lagrangian approach to evolution equations: symmetries and conservation laws.
Journal: Nonlinear Dynamics
Year: 2004
Volume: 36
Issue: 1
Pagination: 29-40
ISSN: 0022-247X
Publisher: KLUWER ACADEMIC PUBL
City: Dordrecht
ISI number: 000222611300004
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
http://www.tek.bth.se/
Authors e-mail: nib@bth.se
Language: English
Abstract: We show that one can apply a Lagrangian approach to certain evolution equations by considering them together with their associated equations. Consequently, one can employ Noether's theorem and derive conservation laws from symmetries of coupled systems of evolution equations. We discuss in detail the linear and non-linear heat equations as well as the Burgers equation and obtain new non-local conservation laws for the non-linear heat and the Burgers equations by extending their symmetries to the associated equations. We also provide Lagrangians for non-linear Schrödinger and Korteweg-de Vries type systems.
Subject: Mathematics\Analysis
Keywords: Differential equations, Lie group analysis, Lagrangian, symmetries, conservation laws
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