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2014 Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms
Weiguo Zhang, Xu Chen, Zhengming Li, Haiyan Zhang
J. Appl. Math. 2014: 1-16 (2014). DOI: 10.1155/2014/963987

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 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.

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Weiguo Zhang. Xu Chen. Zhengming Li. Haiyan Zhang. "Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms." J. Appl. Math. 2014 1 - 16, 2014. https://doi.org/10.1155/2014/963987

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07132024
MathSciNet: MR3216143
Digital Object Identifier: 10.1155/2014/963987

Rights: Copyright © 2014 Hindawi

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