Self-adjointness of a generalized Camassa-Holm equation

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Nail H. Ibragimov, Raisa Khamitova, Antonio Cantoni
Title: Self-adjointness of a generalized Camassa-Holm equation
Journal: Applied Mathematics and Computation
Year: 2011
Volume: 218
Issue: 6
Pagination: 2579-2583
ISSN: 0096-3003
Publisher: Elsevier
URI/DOI: 10.1016/j.amc.2011.07.074
ISI number: 000296278800020
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: It is well known that the Camassa-Holm equation possesses numerous remarkable properties characteristic for KdV type equations. In this paper we show that it shares one more property with the KdV equation. Namely, it is shown in [1,2] that the KdV and the modified KdV equations are self-adjoint. Starting from the generalization [3] of the Camassa-Holm equation [4], we prove that the Camassa-Holm equation is self-adjoint. This property is important, e.g. for constructing conservation laws associated with symmetries of the equation in question. Accordingly, we construct conservation laws for the generalized Camassa-Holm equation using its symmetries.
Subject: Mathematics\General
Keywords: Camassa-Holm equation, Conservation laws, Quasi self-adjointness