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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 925715, 7 pages
http://dx.doi.org/10.1155/2015/925715
Research Article

Orbital Stability of Solitary Traveling Waves of Moderate Amplitude

Department of Mathematics, Foshan University, Foshan, Guangdong 528000, China

Received 2 December 2014; Accepted 24 January 2015

Academic Editor: Stephen C. Anco

Copyright © 2015 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 orbital stability of solitary traveling wave solutions of an equation describing the free surface waves of moderate amplitude in the shallow water regime. Firstly, we rewrite this equation in Hamiltonian form and construct two invariants of motion. Then using the abstract stability theorem of solitary waves proposed by Grillakis et al. (1987), we prove that the solitary traveling waves of the equation under consideration are orbital stable.