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

作　　者：仁世杰 李永军[2] 张娟 REN Shi-jie;LI Yong-jun;ZHANG Juan(School of Information Engineering,Lanzhou City University,Lanzhou Gansu 730070;School of Electronic Engineering,Lanzhou City University,Lanzhou Gansu 730070;School of Mathematics and Computer Science,Ningxia Normal University,Guyuan Ningxia 756000)

机构地区：[1]兰州城市学院信息工程学院,甘肃兰州730070 [2]兰州城市学院电子工程学院,甘肃兰州730070 [3]宁夏师范学院数学与计算机科学学院,宁夏固原756000

出　　处：《甘肃高师学报》2023年第5期18-21,共4页Journal of Gansu Normal Colleges

基　　金：国家自然科学基金“随机动力系统指数吸引子的存在性及其应用研究”(11761044)。

摘　　要：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.

关 键 词：双芯光纤 线性耦合 薛定谔方程 Painlevé检验 

分 类 号：O175.29[理学—数学]