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Conditional stability of solitary wave solutions for generalized nonlinear dissipative hyperelastic-rod wave equation |
Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, Jiangsu 212013, China |
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Abstract Conditional stability of solitary wave solutions for the generalized nonlinear dissipative hyperelasticrod wave equation in the sense of Lyapunov was investigated. Assumping that the tiny disturbance had traveling wave form and met certain conditions, the general solution of the corresponding perturbation equation was obtained. The convergence and divergence of perturbation solution under different parameter conditions and the Lyapunov characteristics index were discussed. The accurate solitary wave solutions of the equation were proved to have conditional stability, and the stability conditions of the solitary wave solution were obtained. These conditions are relationships between system parameters and initial conditions, which means the stability of the solitary wave solution for the equation sensitively depends on system parameters and initial conditions.
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Received: 25 July 2012
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