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| TRAVELINGWAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS |
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Citation： |
Li Jibin,Liu Zhengrong.TRAVELINGWAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS[J].Chinese Annals of Mathematics B,2002,23(3):397~418 |
| Page view： 1555
Net amount： 1164 |
Authors： |
Li Jibin; Liu Zhengrong |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.19731003, No.19961003) and the Yunnan Provincial Natural Science Foundation of China (No.1999A0018M, No.2000A0002M). |
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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. |
Keywords： |
Solitary wave, Periodic wave, Integrable system, Bifurcation of phase portraits, Smoothness of wave |
Classification： |
30D05, 37B55, 35B65 |
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