非线性微分方程的行波解分支

【作者】 纳静；

【导师】 李继彬；

【作者基本信息】 昆明理工大学 ， 应用数学， 2005， 硕士

【摘要】 本文应用动力系统分支理论对一类非线性分数幂方程的动力学行为进行研究,给出了不同参数空间的行波解相图、分支集以及孤立波和扭子波解的存在条件,并得出部分孤立波和扭子波解的精确公式。同时还应用动力系统分支理论对一类修正Camassa-Holm方程进行研究,在参数空间中给定的区域内获得了系统在各种参数条件下可能存在的孤立波解、不可数无穷多光滑和非光滑周期行波解的存在性条件。更多还原

【Abstract】 In this paper, the bifurcation behavior for a class of nonlinear evolution equations is studied by using the method of the bifurcation theory of dynamical systems. The bifurcation sets and phase portraits of the travelling wave equation in the different regions of the parameter space are given. The different parameter conditions for the existence of solitary wave solutions and kink wave solutions are rigorously determined. Explicit formulas of solitary wave solutions and kink wave solutions are given partly. At the same time, by employing the theory of bifurcations of dynamical systems to a modified Camassa-Holm equation, the existence of solitary wave solutions, uncountably infinite many smooth and non-smooth periodic traveling wave solutions, is obtained in the given areas of parametric space.更多还原