广义的Zakharov方程和Ginzburg-Landau方程的精确解和行波解分支

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基金项目: 宁波市自然科学基金资助项目(2008A610029)

Bifurcations of Traveling Wave Solutions and Exact Solutions of Generalized Zakharov Equation and Ginzburg-Landau Equation

School of Information and Art, Ningbo Institute of Education, Ningbo, Zhejiang 315010, P. R. China;

摘要: 获得了广义的Zakharov方程和Ginzburg-Landau方程的一些精确行波解，这些行波解有什么样的动力学行为，它们怎样依赖系统的参数？该文将利用动力系统方法回答这些问题，给出了两个方程的6个行波解的精确参数表达式．
- 动力系统方法 /
- 周期波解 /
- 非线性波方程
Abstract: Some exact traveling wave solutions were found of generalized Zakharov equation and GinzburgLandau equation. What are the dynamical behavior of these traveling wave solutions and how do they depend on the parameters of the systems? These questions by using the method of dynamical systems were answered. Six exact explicit parametric representations of the traveling wave solutions for two equations were given.
- planar dynamical system /
- periodic wave solution /
- nonlinear wave equation

[1]	ZHANG Jin-liang, WANG Ming-liang, GUO Ke-quan. Exact solutions of generalized Zakharov and Ginzburg-Landau equations[J]. Chaos, Solitons and Fractals, 2007,32(5):1877-1886. doi: 10.1016/j.chaos.2005.12.011
[2]	ZHANG Wei-guo, CHANG Qian-shun, FAN En-gui. Methods of judging shape of solitary wave and solution formulae for some evolution equations with nonlinear terms of high order[J]. J Math Anal Appl, 2003, 287(1): 1-18. doi: 10.1016/S0022-247X(02)00336-0
[3]	LIU Cheng-shi. Exact traveling wave solutions for a kind of generalized Ginzburg-Landau equation[J]. Commun Theor Phys, 2005, 43(5):787-790. doi: 10.1088/0253-6102/43/5/004
[4]	LI Ji-bin, CHEN Guan-rong. On a class of singular nonlinear traveling wave equations[J].Int J Bifur Chaos, 2007, 17(11): 4049-4065. doi: 10.1142/S0218127407019858
[5]	LI Ji-bin, DAI HUI-hui. On the Study of Singular Nonlinear Traveling Equations:Dynamical System Approach[M]. Beijing: Science Press, 2007.
[6]	LI Ji-bin, WU Jian-hong, ZHU Huai-ping. Travelling waves for an integrable higher order kdv type wave equations[J]. International Journal of Bifurcation and Chaos, 2006, 16(8):2235-2260. doi: 10.1142/S0218127406016033
[7]	Byrd P F, Fridman M D. Handbook of Elliptic Integrals for Engineers and Scientists[M]. Berlin: Springer, 1971.

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