广义双函数法与求解Davey-Stewartson I方程的解析解

Generalized Double Function Method and Explicit Solutions for Davey-Stewartson I Equation

应用广义双函数法研究了具有物理背景的Davey-StewartsonI方程,通过引入新的基函数、变换和齐次平衡原理,得到了该方程一批新的形式更丰富的显式解.此外,还从理论上证明了齐次平衡原理对该方程组成立.

With generalized double function method, higher-order Davey-Stewartson Ⅰ Equation is studied. By proposing a pair of base functions and using a simple transformation, some explicit solutions are obtained, in which various forms are presented. Furthermore, we have proved that homogeneous balance method is true for Davey-Stewartson Ⅰ Equation. This method was never theoretieally proved in previous reference.