Orbital stability of solitary waves for generalized symmetric regularized-long-wave equations with two nonlinear terms. (English) Zbl 1442.35407

Zhang, Weiguo; Chen, Xu; Li, Zhengming; Zhang, Haiyan

J. Appl. Math. 2014, Article ID 963987, 16 p. (2014).

Summary: 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 \(J\) 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 \(d''(c)\) 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.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35M30	Mixed-type systems of PDEs
35B35	Stability in context of PDEs
35C08	Soliton solutions

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