一类非线性反应-扩散方程丰富的显式精确解

Abundant explicit and exact solutions for a class of nonlinear reaction-diffusion equations

借助于作者最近开发的求解非线性偏微分方程精确解的符号计算软件包——PDE Solver,获得了一类非线性反应-扩散方程丰富的显式精确解.WAZWAZ获得的所有解为本文一些解的特例.另外还获得了许多其他新的显式精确解.结果表明,扩展双曲函数方法是WAZWAZ所提扩展双曲正切方法的改进和推广.扩展双曲函数方法提供了精确求解非线性偏微分方程的有效方法。

With the aid of a computer symbolic software package ＂PDESolver＂, developed by the authors re- cently to solve nonlinear partial differential equations exactly, abundant new exact and explicit solutions of a class of nonlinear reaction-diffusion equation are obtained. All solutions obtained by WAZWAZ are obtained a- gain as special case of some solutions in this paper. Many new explicit and exact solutions are also presented. The results indicated that the extended hyperbolic function method is an extension and improvement to the ex- tended tanh method presented by WAZWAZ. The extended hyperbolic function method provides an effective way to solve nonlinear partial differential equations exactly.