一类KdV非线性Schrdinger组合微分方程组时间周期解的存在性

The Existence of Time Periodic Solutions for a Coupled KdV and Nonlinear Schrdinger Equations

本文研究了一类KdV非线性Schrdinger组合微分方程组时间周期解的问题,首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Leray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性。

The time periodic solution problem of a coupled KdV and nonlinear Schrdinger equations was studied.By using the Galerkin method to construct the approximation sequence of time periodic solutions,a priori estimate and Leray-Schauder fixed point theorem to prove the convergence of the approximate solutions,and obtained the existence of time periodic solutions for a Coupled KdV and Nonlinear Schrdinger Equations.