一类非线性波动方程的显式精确解

Explicit and exact solutions for a class of nonlinear wave equation

借助于未知函数的变换 ,一类非线性非可积波动方程化为易于求解的一个三线性齐次方程 ,从而得到了此类方程的精确扭状孤立波解 ,奇异行波解及周期的三角函数波解 .作为特例 ,Burgers方程 ,Burgers-Huxley方程 ,Chaffee-Infante反应扩散方程 ,Newell-Whitehead方程 ,Fitz Hugh-Nagumo方程的解均可用此法求得 .

with the aid of transformation of an unknown function,a class of nonlinear nonintegrable wave equation are reduced to the trilinear homogeneous equation which can be easily solved, therefore the exact kink shape solitary wave solutions,singular travelling wave solutions,and the periodic triangle function wave solutions are obtained.As special cases,Burgers equation,Burgers Huxley equation, Chaffee Infante reaction diffusion equation,Newell Whitehead equation, FitzHugh Nagumo equation,and an isothermal autocatalytic system equation can also be solved by this method.