(2+1)维非线性波方程的无穷序列JacobiTheta函数解  

JacobiTheta Function Solutions to the Nonlinear Wave Equation in Microstructured Solids

作　　者：毛丽娟[1] 那仁满都拉[2] 

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028043 [2]内蒙古民族大学物理与电子信息学院,内蒙古通辽028043

出　　处：《内蒙古民族大学学报（自然科学版）》2014年第2期128-131,249,共4页Journal of Inner Mongolia Minzu University：Natural Sciences

基　　金：国家自然科学基金资助项目(10862003);内蒙古民族大学科研创新团队建设计划资助项目.

摘　　要：利用JacobiTheta函数满足的恒等关系式,得到了JacobiTheta函数所满足的第一种椭圆方程.以此椭圆方程作为辅助方程,给出了构造非线性偏微分方程精确解的JacobiTheta函数展开方法.利用该方法,并借助第一种椭圆方程的Bcklund变换,获得了(2+1)维非线性波方程的无穷序列JacobiTheta函数解.In this paper, a JacobiTheta function expansion method for solving nonlinear evolution equations is given, taken the identity and the first elliptic equation, which satisfied by JacobiTheta function, as an auxiliary equation. The nonlinear wave equation in microstructured solids is studied by using the method, and many kinds of JacobiTheta func-tion solutions are given. Next infinite sequence solutions are made by the method of B？cklund transformation.

关 键 词：JacobiTheta函数展开法 非线性波方程 无穷序列解 BACKLUND变换 

分 类 号：O175.2[理学—数学]