用改进的试探函数法求解广义KdV方程  

Solving the Generalized KdV Equation by Applying the Improved Trial Function Method

作　　者：谢元喜[1] 

机构地区：[1]湖南人文科技学院物理与信息工程系,湖南娄底417000

出　　处：《湖南人文科技学院学报》2006年第3期13-15,共3页Journal of Hunan University of Humanities,Science and Technology

摘　　要：试探函数法求解非线性数学物理中一个非常著名的非线性偏微分方程—广义KdV方程,求得其一般形式的指数函数解,据此不但求得了广义KdV方程的sech2型钟状正则孤波解,而且求得了其csch2型奇异行波解,最后,利用一些熟知的数学关系式,又求得其若干其它显式精确解,包括三角函数型周期波解等。We make two distinct and different modifications of the trial function method put forward in Ref. As a consequence, by taking full advantage of this improved trial function method, we may find the more general solution of the exponential function form for the well-known generalized KdV equation in nonlinear mathematical physics in a concise and direct manner. On the basis of it, not only the sech2-type bell - profile regular solitary wave solution but also the csch2-type singular travelling wave solution with importantly physical significance of the generalized KdV equation is able to be readily found. At last, with the bell- profile some well-known mathematical formulae, we may still find a lot of other explicit and exact solutions to the generalized KdV equation, which include trigonometric function periodic wave solutions and the like.

关 键 词：改进的试探函数法 广义KDV方程 指数函数解 钟状正则孤波解 奇异行波解 三角函数型周期波解 

分 类 号：O241.8[理学—计算数学]