Fisher方程的有界衰减振荡解
Bounded damped oscillatory solutions of Fisher equation
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摘要: 为了研究非线性发展方程的有界衰减振荡解,特选取Fisher方程为例.Fisher方程在描述激发介质的非数值模型(如Belousov-Zhabotinsky(Bz)反应)中,其解的振幅取负值是有意义的.应用平面动力系统理论,研究了Fisher方程有界行波解存在的条件,利用LS解法和线性化解法给出了其有界衰减振荡解的近似解析表达式,并进行了误差估计.Abstract: To research the bounded damped oscillatory solutions of nonlinear evolution equation, we choose the Fisher equation as an example. The solutions with negative amplitudes of Fisher equation may become meaningful in the context of nonscalar models describing excitable media (e.g. the Belousov-Zhabotinsky (BZ) reaction). The theory of planar dynamical systems is used to study the existence conditions of bounded traveling wave solutions of Fisher equation. The bounded approximate damped oscillatory analytic solution is given by using LS method and linearization method. And its error is also estimated.
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