Davey-Stewartson Ⅰ方程新的精确周期解  

New Exact Periodic Solutions for the Davey-Stewartson Ⅰ equation

作　　者：刘常福[1] 戴正德[2] 

机构地区：[1]云南省文山师范高等专科学校数理系,文山663000 [2]云南大学数学与统计学院,昆明650091

出　　处：《工程数学学报》2008年第3期510-514,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10361007,10661002);云南省自然科学基金(02004A0001M);云南省教育厅基金(06Y041A).

摘　　要：Davey-Stewartson方程描述了有限深度的水中水波的运动,它的第一种类型称为(Davey-Stewartson I)是椭圆一双曲型方程。在物理学中,微分方程的精确解对考察非线性现象起着非常重要的作用,为了揭示Davey-Stewartson I方程的运动性质,本文研究它的精确周期解。应用F-代数方法并通过一个高阶辅助微分方程,获得了Davey-Stewartson I方程的一系列新的精确周期解,包括三角函数周期解,Jacobi椭圆函数周期解。One of the Davey-Stewartson equations describing two-dimensional surface waves on water of finite depth is the elliptic-hyperbolic equation, denoted as Davey-Stewartson Ⅰ. Exact solution of differential equations have played a significant role in our understanding of nonlinear phenomena in physics. To understand wave propagation properties of the Davey-Stewartson Ⅰ equation, we investigate its exact periodic solutions in this paper. The F-algebraic method and a high order auxiliary differential equation are used to derive a series of new exact periodic solutions including triangular function periodic solutions and Jacobi elliptic function periodic solutions.

关 键 词：DAVEY-STEWARTSON Ⅰ方程 F-代数方法 三角函数周期解 Jacobi椭圆函数周期解 

分 类 号：O175.29[理学—数学]