一类耦合非线性薛定谔方程组的求解

Solving a Class of Coupled Nonlinear Schr dinger Equations

在可积条件[HJ41x]c(t)=(γ2(t))2=1(C 1t+C 2)2,γ1(t)=γ2(t)=1 C 1t+C 2下,利用特殊变换法和Sine-cosine方法,得到了双芯光纤变系数线性耦合薛定谔方程组i∂∂t u(x,t)+i∂∂x u(x,t)-∂2∂t 2 u(x,t)+γ1(t)u(x,t)2u(x,t)+c(t)v(x,t)=0,i∂∂t v(x,t)+i∂∂x v(x,t)-∂2∂t 2 v(x,t)+γ2(t)v(x,t)2v(x,t)+[HJ]c(t)u(x,t)=0的精确解.其中:C i(i=1,2)是常数;γi(t)(i=1,2)是第i个纤芯的非线性参数;c(t)是两个纤芯之间的线性耦合参数.

In this paper,the exact solutions of the linearly coupled nonlinear Schr dinger Equation Group i∂∂t u(x,t)+i∂∂x u(x,t)-∂2∂t 2 u(x,t)+γ1(t)u(x,t)2u(x,t)+c(t)v(x,t)=0 i∂∂t v(x,t)+i∂∂x v(x,t)-∂2∂t 2 v(x,t)+γ2(t)v(x,t)2v(x,t)+c(t)u(x,t)=0 with variable coefficients of two-core fiber are calculated by special transformation method and method under integrable condition c(t)=(γ2(t))2=1(C 1t+C 2)2γ1(t)=γ2(t)=1 C 1t+C 2 among which C i(i=1,2)is the constant,γi(t)is the nonlinear parameters of the i-thcore and c(t)is the linear coupling parameters between the two cores.