用形变映射法求KdV方程的显式精确行波解  

Searching for Explicit Traveling Wave Solutions of KdV Equation by Deformation Mapping Method

作　　者：钟太勇[1] 钟远涛[1] 

机构地区：[1]郧阳师范高等专科学校数学系,湖北十堰442700

出　　处：《江汉大学学报（自然科学版）》2009年第3期10-12,共3页Journal of Jianghan University：Natural Science Edition

摘　　要：利用形变映射法建立KdV方程与非线性Klein-Gordon(NKG)方程的一类特殊类型解的代数变换关系.根据NKG方程的已知解,获得KdV方程系统丰富的显式精确行波解,包括孤波解、周期波解,Jacobi椭圆函数解.Deformation mapping method is applied to obtain exact solutions of the KdV equation. A simple algebraic transformation relation of a special type of solution between the KdV equation and the cubic nonlinear Klein-Gordon （NKG） equation is established by deformation mapping method. With the aid of this relation and known solutions of the KdV equation, abundant explicit and exact traveling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobi elliptic function solutions and others exact solutions, are obtained.

关 键 词：形变映射法 KDV方程 非线性Klein-Gordon(NKG)方程 行波解 

分 类 号：O175.24[理学—数学]