一类二次KdV类型水波方程的行波解

龙瑶; 李继彬; 芮伟国; 何斌

一类二次KdV类型水波方程的行波解

1.
红河学院数学系,云南蒙自 661100;2.浙江师范大学数学系,浙江金华 321004;3.昆明理工大学理学院,昆明 650093

基金项目: 国家自然科学基金资助项目(10231020);云南省自然科学基金资助项目(2003A0018M);云南省教育厅科学研究基金重点资助项目(5Z0071A)

详细信息

作者简介:
龙瑶(1957- ),女,云南西盟人,教授(联系人.Tel:+86-873-3699239;E-mail:yaolong04@163.com).

中图分类号: O175.12
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- 被引次数: 0
出版历程
- 收稿日期: 2006-02-28
- 修回日期: 2007-09-17
- 刊出日期: 2007-11-15

Travelling Wave Solutions for a Hight Order Wave Equation of KdV Type

1.
Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, P. R. China;

摘要

摘要: 应用平面动力系统理论研究了一类非线性KdV方程的行波解的动力学行为．在参数空间的不同区域内,给出了系统存在孤立波解,周期波解,扭子和反扭子波解的充分条件,并计算出所有可能的精确行波解的参数表示．
- 孤立波解 /
- 周期波解 /
- 扭子波和反扭子波解 /
- 光滑和非光滑周期波
Abstract: The theory of planar dynamical systems is used to study the dynamical behaviour of the travelling wave solutions of a nonlinear wave equations of KdV type. In different regions of the parametric space, sufficient conditions to guarantee the existence of solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions are given. All possible exact explicit parametric representations are obtained for these waves.
- solitary wave solution /
- periodic wave solution /
- kink wave and anti-kink wave solutions /
- smooth and non-smooth periodic wave

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参考文献(12)

[1]	Tzirtzilakis E,Xenos M,Marinakis V,et al.Interactions and stability of solitary waves in shallow water[J].Chaos, Solitons and Fractals,2002,14(1):87-95. doi: 10.1016/S0960-0779(01)00211-9
[2]	Tzirtzilakis E,Marinakis V,Apokis C,et al.Soliton-like solutions of higher order wave equations of the Korteweg-de-Vries type[J].J Math Phys,2002,43(12):6151-6161. doi: 10.1063/1.1514387
[3]	Fokas A s.On a class of physically important integralequations[J].Physica D,1995,87(1/4):145-150. doi: 10.1016/0167-2789(95)00133-O
[4]	LONG Yao,RUI Wei-guo,HE Bin.Travelling wave solutions for a higher order wave equations of KdV type (Ⅰ)[J].Chaos, Solitons and Fractals,2005,23(2):469-475. doi: 10.1016/j.chaos.2004.04.027
[5]	LI Ji-bin,DAI Hui-hui.On the studies of sigular travelling wave equations[A].Dynamical System Approach[C].Beijing:Science Press, 2007.
[6]	Chow S N,Hale J K.Method of Bifurcation Theory[M].New York:Springer-Verlag,1981.
[7]	Guckenheimer J,Holmes P J.Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields[M].New York:Springer-Verlag, 1983.
[8]	Perko L.Differential Equations and Dynamical Systems[M].New York:Springer-Verlag,1991.
[9]	Li Y A,Olver P J.Convergence of solitary-wave solutionsin a perturbed bi-Hamiltonian dynamical system Ⅰ:Compactons and peakons[J].Discrete and Continuous Dynamical Systems,1997,3(3):419-432. doi: 10.3934/dcds.1997.3.419
[10]	Li Y A,Olver P J.Convergence of solitary-wave solutionsin a perturbed bi-Hamiltonian dynamical system Ⅱ: Complexanalytic behaviour and convergence to non-analytic solutions[J].Discrete and Continuous Dynamical Systems,1998,4(1):159-191.
[11]	LI Ji-bin,LIU Zhen-rong.Smooth and non-smooth travelling waves in a nonlinearly dispersive equation[J].Appl Math Modelling,2000,25(1):41-56. doi: 10.1016/S0307-904X(00)00031-7
[12]	LI Ji-bin,LIU Zhen-rong.Travelling wave solutions for a class of nonlinear dispersive equations[J].Chin Ann of Math,2002,23B(3):397-418.