International Journal of Differential Equations
Volume 2011 (2011), Article ID 738509, 13 pages
http://dx.doi.org/10.1155/2011/738509
Research Article

Geometric Integrability of Some Generalizations of the Camassa-Holm Equation

Ognyan Christov

Faculty of Mathematics and Informatics, Sofia University, 5 J. Bouchier boulevard., 1164 Sofia, Bulgaria

Received 27 May 2011; Accepted 17 July 2011

Academic Editor: V. A. Yurko

Copyright © 2011 Ognyan Christov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the Camassa-Holm (CH) equation and recently introduced μCH equation from the geometric point of view. We show that Kupershmidt deformations of these equations describe pseudospherical surfaces and hence are geometrically integrable.