反应扩散方程的几何分支和真解研究

Bifurcation Analysis and Some Exact Solutions of Reaction-Diffusion Equations

本文的主要目的在于研究反映扩散方程的动力学行为和真解。我们利用几何分支理论讨论了平衡点的类型和相应的相轨线分布。特别的,我们利用分离变量方法得到了方程的一些新的解析解,另外,我们还讨论了行波解和相轨线之间的对应关系。

The purpose of this paper is to reveal the dynamical behavior and exact solutions of the reac一tion一diffusion equations. We employ bifurcation theory to discuss the type of equilibrium points, and correspondingphase orbits are derived. Specially, some new analytical solutions are gained by using variable separation method. Inaddition, we discuss the correspondence between the travelling wave solutions and phase orbits.