两个非线性发展方程组精确解析解的研究  

Study on Exact Analystical Solutions for Two Systems of Nonlinear Evolution Equations

作　　者：闫振亚[1] 张鸿庆[1] 

机构地区：[1]大连理工大学应用数学系,大连116024

出　　处：《应用数学和力学》2001年第8期825-833,共9页Applied Mathematics and Mechanics

基　　金：国家重点基础研究规划项目 (G19980 30 60 0 ) ;教育部博士点基金资助项目 ( 980 14119)

摘　　要：对齐次平衡法进行了改进并将其应用于两个非线性发展方程组中·　通过一些新的假设 ,获得了若干精确解析解·　这些解包含王和张的结论及其它新类型的解析解 ,如有理分式解和周期解·　这种方法也可以应用于求解更多的非线性偏微分方程·The homogeneous balance method was improved and applied to two systems of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations.

关 键 词：非线性发展方程 齐次平衡法 周期解 精确解析解 孤波解 有理解 长波近似方程 

分 类 号：O175.14[理学—数学]