摘要
介绍一种求解非线性偏微分方程行波解的方法,运用这种方法获得mkdv方程的行波解.在求解方程的过程中,引入一个变元u(x,t)=u(ξ)=u[k(x-ωt)]并代入方程,进行简单的求偏导数运算,将难以解决的非线性偏微分方程化为易于求解的代数方程,最后得到方程的行波解.这种方法还可推广到高维非线性演化方程求解.
A method to solve nonlinear partial differential equations is introduced,and traveling wave solutions of mkdv equation are obtained.By means of recommending a variable,and partial derivation into equation are taken,then traveling wave solutions of equation are obtained by transforming difficult nonlinear partial differential equation into easy algebraic equation.This method can also be used to solve high-dimensional nonlinear evolution equations.
出处
《渭南师范学院学报》
2012年第10期15-18,共4页
Journal of Weinan Normal University
基金
陕西省教育厅专项科研计划项目(2010JK535)
陕西省军民融合研究基金项目(11JMR08)
渭南师范学院科研计划项目(11YKZ004)
关键词
精确解
行波解
直接方法
MKDV方程
exact solutions
traveling wave solutions
direct method
mkdv equation
