累次齐次平衡法及其应用  

The Repeated Homogeneous Balance Method and Its Applicatons

作　　者：丁双双[1] 孙维君[2] 

机构地区：[1]中国海洋大学数学系,山东青岛266071 [2]山东理工大学物理与光电信息技术学院,山东淄博255049

出　　处：《数学的实践与认识》2008年第12期127-135,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10272068)

摘　　要：在求非线性偏微分方程精确解的过程中两次使用了齐次平衡法(称为累次齐次平衡法),解决了齐次平衡法求解少的不足,从而改进了齐次平衡法.以高阶(2+1)维Kadomtsev-Petviashvili方程和变异的Boussinesq方程为应用实例,说明使用累次齐次平衡法可以求得大量的精确解,其中许多解是新解或覆盖了其他方法所得的解.方法可应用于大量的非线性物理模型.The homogeneous balance method is applied twice and then improved to construct the exact traveling wave solutions of nonlinear partial differential equations （called the repeated homogeneous balance method）. As two illustrative equations, （2＋1）-dimensional Kadomtsev- Petviashvili equation and variant Boussinesq equations are investigated by the repeated homogeneous balance method, and a lot of their exact traveling wave solutions are obtained, in which many solutions are new and more general types of solutions. The repeated homogeneous balance method can be used to solve lots of nonlinear physical model.

关 键 词：累次齐次平衡法 齐次平衡法 精确行波解 

分 类 号：O175.29[理学—数学] P731.22[理学—基础数学]