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微扰KdV方程的精确解 被引量:3

Exact solutions for KdV equation with perturbation terms
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摘要 研究了含有各种形式微扰项的KdV方程,利用试探函数法构造它们新的精确解.通过观察与尝试,对解的形态作预先假设,代入原方程,将一个难于求解的非线性偏微分方程化为一组易于求解的非线性代数方程,然后用待定系数法确定相应的常数,最后求得了含有各种形式微扰项的KdV方程的精确解. First,this paper studied KdV equation with perturbation terms in different forms by using the trial function method to construct some new exact solutions for them.By observing and attemptting,the paper supposed in advance the form of the solution,which was substituted into the original equation,and divided the difficult nonlinear partial differential equation into a group of easy nonlinear algebraic equation.Then,the corresponding constant with the undetermined coefficient law was determined.Finally,exact analytic solution of KdV equation with perturbation terms in different forms was obtained.
出处 《河南理工大学学报(自然科学版)》 CAS 2010年第4期551-554,共4页 Journal of Henan Polytechnic University(Natural Science)
基金 河南省高校科技创新人才支持计划(2009-HASTTT-007) 河南理工大学青年基金资助项目(Q200931)
关键词 微扰KdV方程 精确解 试探函数法 KdV equation with perturbation terms exact solution trial function method
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