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Methods of judging shape of solitary wave and solution formulae for some evolution equations with nonlinear terms of high order |
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| Authors: | Weiguo Zhang Engui Fan |
| Affiliation: | a Department of Basic Sciences, University of Shanghai for Science and Technology, Shanghai 200093, PR China b Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, The Chinese Academy of Sciences, Beijing, 100080, PR China c Institute of Mathematics, Fudan University, Shanghai 200433, PR China |
| Abstract: | In this paper, we present several methods of judging shape of the solitary wave and solution formulae for some nonlinear evolution equations by means of Lienard equations. Then, using the judgement methods and solution formulae, we obtain solutions of the solitary wave for some of important nonlinear evolution equations, which include generalized modified Boussinesq, generalized nonlinear wave, generalized Fisher, generalized Klein-Gordon and generalized Zakharov equations. Some new solitary-wave solutions are found for the equations. |
| Keywords: | Solitary wave Exact solution Generalized modified Boussinesq equation Generalized nonlinear wave equation Generalized Fisher equation Generalized Klein-Gordon equation Generalized Zakharov equation |
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