Fisher方程行波解的定性分析及线性化解法

Qualitative Analysis and Linearization Method of Traveling Wave Solutions of Fisher Equation

物理学、化学和生物学中存在大量的反应扩散现象,著名的Fisher方程就是描述该类现象的一类反应扩散方程。将Fisher方程经行波约化后化为等价的平面自治系统,而后对其有限处奇点、无穷远奇点及闭轨的存在性进行了定性分析,并用线性化解法求解得到其特殊的积分曲线,从而也得到了波速c=±56/6时Fisher方程的波前解。

There exist numerous reaction-diffusion phenomena in physics,chemistry and biology.The well-known Fisher equation is one of the reaction-diffusion equations that describe such phenomena.The traveling wave reduction ODE to the Fisher equation is reduced to an equivalent autonomous plane system.The finite singular points,the infinite singular points and the existence of closed orbit of the system are qualitatively analyzed.The particular integral curves are obtained by means of linearization method,thus the explicit wave front solutions with a special wave speed(c=±56/6)are obtained.