三分量耦合DNLS方程的高阶孤子解  

Study on High-Order Soliton Solutions of the Three-Component Coupled Derivative Nonlinear Schrodinger Equation

作　　者：郭明敏 刘然 宋妮[1] GUO Ming-min;LIU Ran;SONG Ni(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《数学的实践与认识》2023年第12期218-224,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11602232,12372026);山西省回国留学人员科研资助项目(2022-150);山西省自然科学基金(202203021211086,202203021211088)。

摘　　要：基于一个含有导数项的三分量耦合非线性薛定谔方程,利用经典Darboux变换,对函数进行泰勒展开,推导出广义Darboux变换.在方程对应的Lax对和广义Darboux变换的基础上,得到方程高阶孤子解的表达式.分情况讨论谱参数λ的实部与虚部,对孤子解表达式中的自由参数取不同的值,分析参数对二阶、三阶孤子之间弹性、非弹性碰撞的影响.通过数值模拟,得到孤子相互作用演化图,进一步对孤子的动力学特性进行分析,结果对耦合DNLS方程具有重要的参考意义.Based on a three-component coupled derivative nonlinear Schrodinger(DNLS)equation,a generalized Darboux transformation is derived by Taylor expansion of the function via the classical Darboux transformation.On the basis of the Lax pairs and the generalized Darboux transformation,the expression for the higher-order soliton solution of the equation is obtained.The real part and imaginary part of the spectral parameters are discussed in different cases,and the dynamic characteristics of elastic and inelastic collisions between second-order and third-order solitons are analyzed according to different values of free parameters in the iterative expression.The results are of great significance to the threecomponent coupled derivative nonlinear Schrodinger equation.

关 键 词：含有导数项的耦合非线性薛定谔方程 广义Darboux变换 孤子解 

分 类 号：O175.29[理学—数学]