一类非线性耦合微分方程的行波解分支
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摘要
本文运用动力系统的分支理论对一类非线性耦合微分方程的动力学行为进行研究,对于不同的参数条件给出了行波解的相图分支,及孤波解、扭结波解和反扭结波解存在的各种充分条件,并给出了部分孤立波和扭结波的精确解。
By using the theory of bifurcations of dynamical systems to a system of coupled nonlinear equations, the existence of solitary wave solutions, kink wave solutions and anti-kink wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.
By using the theory of bifurcations of dynamical systems to a system of coupled nonlinear equations, the existence of solitary wave solutions, kink wave solutions and anti-kink wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.
引文
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[2]. Guckenheimer, J. and Holmes,P.J. Nonlinear oscillations, dynamical systems and bifurcations of vector fields, New York, Springer-Verlag,1983.
[3]. Guha-Roy, C. Solitary wave solutions of system of coupled nonlinear equations, J.Math.Phys. 28(1987)(9):2087-2088.
[4]. Li Jibin and Liu Zhengrong, Smooth and non-smooth traveling waves in a nonlinearly dispersive equation. Appl. Math. Modelling 25(2000): 41-56.
[5]. Li Jibin and Liu Zhengrong, Traveling waves solutions for a class of nonlinearly dispersive equations. Chinese Ann Math Ser B23(2002)(3): 397-418.
[6].李继彬.混沌与Melnikov方法.重庆大学出版社.1991.
[7].李继彬,冯贝叶.稳定性,分支与混沌.云南科技出版社.1995.3.
[8].唐云.对称性分岔理论基础.科学出版社.1998.3.
[9].罗定军,张祥,董艳芳.动力系统的定性与分支理论.科学出版社.2001.2.
[10].张锦炎,冯贝叶.常微分方程几何理论与分支问题.北京大学出版社.200.3.