分离变量法在变系数(2+1)维方程求解中的应用  

The Application of the Variable Separation Method to the Variable-Coefficient(2+1)-dimensional Equation

作　　者：孟祥花[1] 许瑞麟[1] 许晓革[1] 

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《数学的实践与认识》2014年第16期282-287,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61072145);北京市优秀人才项目(2013D005007000003);北京市教委科技计划面上项目(SQKM201211232016)

摘　　要：分离变量法是求解具有局域相干结构解的有效解析方法.考虑到传播介质的非均匀性和边界的不一致性,变系数(2+1)色散长波方程可以实际地描述宽广的河道或有限深的远海中非线性波的传播.解析研究了变系数(2+1)维色散长波方程.通过分离变量法,得到了该方程组的具有丰富结构的分离变量解.The variable separation method is one effective analytical method to solving the localized coherent structure solutions of the nonlinear partial differential equation. Con- sidering the inhomogeneous of the media and the uniformity of the boundary, the variable- coefficient （2＋1）-dimensional dispersive long wave equations can describe the situation in wide channels or open seas of finite depth realistically. In this paper, the variable-coefficient （2＋1）-dimensional dispersive long wave equation is investigated analytically. Through the variable separation approach, variable separation solutions with abundant structures for the （2＋1）-dimensional variable-coefficients dispersive long wave equation have been presented.

关 键 词：变系数(2+1)色散长波方程 分离变量法 分离变量解 

分 类 号：O241.7[理学—计算数学]