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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 789269, 6 pages
http://dx.doi.org/10.1155/2015/789269
Research Article

Stability of Negative Solitary Waves for a Generalized Camassa-Holm Equation with Quartic Nonlinearity

1Department of Basic Courses, Guangzhou Maritime Institute, Guangdong 510725, China
2Department of Mathematics, Foshan University, Guangdong 528000, China

Received 6 October 2015; Revised 1 December 2015; Accepted 8 December 2015

Academic Editor: Christian Engstrom

Copyright © 2015 Shan Zheng and Zhengyong Ouyang. 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 consider the stability of negative solitary waves to a generalized Camassa-Holm equation with quartic nonlinearity. We obtain the existence of negative solitary waves for any wave speed and some of their qualitative properties and then prove that they are orbitally stable by using a method proposed by Grillakis et al.