一类非线性耦合系统的不稳定性质

The Instability of a Class of Nonlinear Coupled System

讨论一类描述电磁波相互作用的非线性Schr dinger方程耦合系统iψt+Δψ+ψF(｜ψ｜2)=ψθ, -Δθ+a2θ=｜ψ｜2,其中,ψ(x,t)和θ(x,t)分别为复值和实值函数,a∈R,x∈Rn,t>0的初值问题,得到了在一定条件下解的不稳定性质.

In this paper, we study a class of coupled system of the nonlinear Schrdinger equations as follows,iψt+Δψ+ψF(|ψ|2)=ψθ,-Δθ+a2θ=|ψ|2,which describe the interaction of electromagnetic wave:where ψ(x,t) and θ(x,t) are complex and realvalue functions respectively and a∈R,x∈Rn,t>0. The instability of the solution of the system is obtained.