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Journal of Applied Mathematics
Volume 2014, Article ID 963987, 16 pages
http://dx.doi.org/10.1155/2014/963987
Research Article

Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms

1College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 28 February 2014; Accepted 8 May 2014; Published 26 May 2014

Academic Editor: Wan-Tong Li

Copyright © 2014 Weiguo Zhang et al. 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

This paper investigates the orbital stability of solitary waves for the generalized symmetric regularized-long-wave equations with two nonlinear terms and analyzes the influence of the interaction between two nonlinear terms on the orbital stability. Since is not onto, Grillakis-Shatah-Strauss theory cannot be applied on the system directly. We overcome this difficulty and obtain the general conclusion on orbital stability of solitary waves in this paper. Then, according to two exact solitary waves of the equations, we deduce the explicit expression of discrimination and give several sufficient conditions which can be used to judge the orbital stability and instability for the two solitary waves. Furthermore, we analyze the influence of the interaction between two nonlinear terms of the equations on the wave speed interval which makes the solitary waves stable.