(2+1)维色散长波方程的扩展椭圆函数有理展开解法  

THE METHOD OF SOLVING (2+1)-DIMENSIONAL DISPERSIVE LONG WAVE EQUATION WITH EXTENDED ELLIPTIC FUNCTION RATIONAL EXPANSION

作　　者：向以华[1] 石义霞[2] 

机构地区：[1]重庆三峡学院数学与计算机学院,重庆万州404000 [2]湛江师范学院数学与计算机科学学院,广东湛江524048

出　　处：《数学杂志》2009年第2期206-210,共5页Journal of Mathematics

基　　金：重庆市教委科技计划项目(KJ09110X);重庆三峡学院科研项目(SXXYYB08XX)

摘　　要：在一个新的更一般的假设下,借助于符号计算,提出了一个椭圆函数有理展开法,并用它统一地求出许多非线性发展方程新的双周期精确解.本文选择(2+1)维色散长波方程作为此方法的应用来加以说明.得到了Yan方法所得的所有解,并且得到更多的一般形式的解.在m取它的极限时,可得到许多冲击波解和孤立波解.In this paper, a rational elliptice function method is given by symbolic computation expansion method and a new hypothesis. Moreover, the method is quoted to obtain the new double-periodic exact solutions of many nonlinear evolution equations uniformly. To apply this method we choose the （2 -t- 1 ）- dimensional dispersive long wave equation. The result shows that we get all the solutions that Yan received by his method. Simultaneously, more general formal solutions are derived when using the limit of m, we can have many solitary wave solutions and soliton solutions.

关 键 词：2+1维色散长波方程 Weierstrass和Jacobi椭圆函数 行波解 孤立波 

分 类 号：O175.29[理学—数学]