TRAVELINGWAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS |
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| Authors: | Li Jibin and Liu Zhengrong |
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| Institution: | Center for Nonlinear Science Studies, Kunming University of Science and Technology and Institute of Applied Mathmatics of Yunnan Province, Kunming 650093, China.;Department of Mathematics, Yunnan University and Institute of Applied Mathematics of Yunnan Province, Kunming 650091, China. |
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| Abstract: | The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations. By using the bifurcation theory of dynamical systems to do qualitative analysis, all possible phase portraits in the parametric space for the traveling wave systems are obtained. It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied. The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined. |
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| Keywords: | Solitary wave Periodic wave Integrable system Bifurcation of phase portraits Smoothness of wave |
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