| TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS |
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| 作者姓名： | Li Jibin Liu Zhengrong |
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| 作者单位： | LI JIBIN Center for Nonlinear Science Studies，Kunming University of Science and Technology and Institute of Applied Mathmatics of Yunnan Province，Kunming 650093，China. LIU ZHENGRONG Department of Mathematics，Yunnan University and Institute of Applied Mathematics of Yunnan Province，Kunming 650091，China. |
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| 基金项目： | National Natural Science Foundation of China(No.19731003,No.19961003)，Yunnan Provincial Natural Science Foundation of China(No.1999A0018M,No.2000A0002M) |
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| 摘 要： | The method of the phase plane is emploied to investigate the solitary and periodic travelingwaves for a class of nonlinear dispersive partial differential equations.By using the bifurcationtheory of dynamical systems to do qualitative analysis,all possible phase portraits in theparametric space for the traveling wave systems are obtained.It can be shown that the existenceof a singular straight line in the traveling wave system is the reason why smooth solitary wavesolutions converge to solitary cusp wave solution when parameters are varied.The differentparameter conditions for the existence of solitary and periodic wave solutions of different kindsare rigorously determined.
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| 关 键 词： | 行波解 非线性扩散方程 相平面 孤波 周期性 偏微分方程 分歧理论 光滑性 存在性 参数 可积系统 跳跃 |
| 收稿时间： | 1/1/2009 12:00:00 AM |
TRAVELINGWAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS |
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| Li Jibin,Liu Zhengrong.TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS[J].Chinese Annals of Mathematics,Series B,2002,23(3):397-418. |
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| Authors: | Li Jibin and Liu Zhengrong |
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| Institution: | 1. Center for Nonlinear Science Studies,Kunming University of Science and Technology and Institute of Applied Mathmatics of Yunnan Province,Kunming 650093,China.2 Department of Mathematics,Yunnan University and Institute of Applied Mathematics of Yunnan Prov
2. 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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