一类耦合非线性薛定谔方程组的Painlevé分析

PainlevéAnalysis for a Class of Coupled Nonlinear Schrodinger Equation

通过Painlevé检验方法得到了当非线性参数γ_1(t)与γ_2(t)相等,线性耦合参数等于非线性参数的平方且γ_(i)(t)=1/(C_(1)t+C_(2))(i=1,2)时,方程组■是Painlevé可积的,其中C_(1)和C_(2)是任意常数.此方程是来自非线性光学的变系数线性耦合的非线性薛定谔方程组,其中,γ_i(t)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.

By means of Painlevétest method,it is obtained that when the nonlinear parameterγ_(1)(t)is equal toγ_(2)(t)and the linear coupling parameter is equal to the square of the nonlinear parameter and satisfiesγ_(2)(t)=1/(C_(1)t+C_(2))(i=1,2),the system■is Painlevéintegrable,where C_(1) and C_(2) are an arbitrary constant.This equation is a variable coefficient linearly coupled nonlinear Schr?dinger equation system from nonlinear optics.γ_i(t)is the nonlinear parameters of the j-th core and c(t)is the linear coupling parameters between the two cores.