形变映射法求非线性方程的行波解  

Searching for traveling wave solutions of nonlinear equations bymeans of deformation mapping approach

作　　者：吴涛[1] 陈贻汉[1] 熊艳[1] 

机构地区：[1]湖北大学物理学与电子技术学院,湖北武汉430062

出　　处：《湖北大学学报（自然科学版）》2005年第2期104-108,共5页Journal of Hubei University：Natural Science

摘　　要：利用形变映射法,借助于计算机代数系统,得到一类非线性波动方程与非线性Klein-Gordon(NKG)方程特殊类型解之间的代数变换关系,由此获得了这类方程丰富的显式精确行波解,并且由这些解再次映射出了Boussinesq方程的行波解,并给出了波动图形及相关分析.Deformation mapping approach is applied to solving a type of nonlinear wave equations .With the aid of computer algebraic system, a simple algebraic transformation relation between a special type of solution of the nonlinear Klein-Gordon(NKG) equation and the nonlinear wave equation is obtained. Thus, abundant explicit and exact traveling wave solutions of the class of nonlinear wave equation are obtained. Using the results above, the wave solutions of nonlinear Boussinesq equation are also found by means of the method . Thereafter the figures of the traveling wave solutions and related analysis are given.

关 键 词：非线性演化方程 形变映射法 计算机代数系统 BOUSSINESQ方程 

分 类 号：O175[理学—数学]