Jacobi椭圆函数展开法及其应用  

Expansion Method about the Jacobi Elliptic Function and Its Applications

作　　者：王晓丽[1] 张鸿庆[1] 

机构地区：[1]大连理工大学应用数学系,辽宁大连116024

出　　处：《烟台大学学报（自然科学与工程版）》2003年第2期94-98,共5页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(10072013);国家重点基础研究发展规划资助项目(G1998030600).

摘　　要：借助于计算机代数和吴方法,本文给出了一种求非线性波动方程精确解的方法———Jacobi椭圆函数展开法.此方法改进了已有的Jacobi椭圆正弦函数和Jacobi椭圆余弦函数展开法.应用此方法,本文不仅得到了KdV方程、Boussinesq方程以及Klein Gordon方程的已有的实数解,还给出了新的复数解.在它们的极限条件下,新的周期波解和冲击波解也被获得.With the assistance of computer algebra and Wu's method,a Jacobi elliptic function expansion method is proposed to solve the exact solutions of nonlinear wave equations. The method improves the existing Jacobi elliptic sine function method and the Jacobi elliptic cosine function method. Not only the real solutions of KdV equations, Boussinesq equations and KleinGordon quations are obtained by this method, but also their new complex solutions are obtained. Under their limits, some new periodic solutions and shock waves solutions are also obtained.

关 键 词：非线性波动方程 精确解 JACOBI椭圆函数展开法 计算机代数 吴方法 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]