非线性Schrōdinger方程和非线性Klein-Gordon方程耦合组Cauchy问题整体经典解的存在唯一性

UNIQUENESS AND GLOBAL EXISTENCE THEOREM OF SOLUTION FOR Cauchy PROBLEM FOR NONLINEAR Klein-Gordon EQUATION AND NONLINEAR Schrodinger EOUATION COUPLING SYSTEM

本文讨论非线性Schrōdinger方程和非线性Klein-Gordon方程耦合组的Cauchy问题,对初值和空间维数以及非线性项加以适当限制,在Sobolev空间框架下,得到了整体经典解的存在唯一性。

In this paper, a Cauchy problem for nonlinear Klein-Gordon equation and nonlinear Schrodinger equation coupling system is discussed. In the frame of Sobolev space, we obtained the existence and the uniqueness of global solution by using fixed-point principles, under some restrictions on initial data, space dimention and nonlinear term.