耦合Kundu-Eckhaus方程的局域波解及其动力学特性  

The Localized Wave Solutions and Its Dynamical Characteristics of a Coupled Kundu-Eckhaus Equation

作　　者：刘然 郭明敏 宋妮[1] LIU Ran;GUO Mingmin;SONG Ni(School of Mathematics,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：《中北大学学报（自然科学版）》2023年第6期583-590,共8页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11602232);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资助项目(202203021211086,202203021211088)。

摘　　要：基于广义Darboux变换研究了三分量耦合Kundu-Eckhaus方程的局域波解并分析了其动力学特性。首先,根据耦合Kundu-Eckhaus方程的Darboux矩阵和Lax对,利用广义Darboux变换得到局域波解的迭代表达式。然后对表达式中的参数进行分类讨论,揭示了怪波与孤子和呼吸子之间的相互作用。通过数值模拟得到了一阶和二阶局域波演化图,进一步分析了局域波的动力学特性。结果表明,对参数取不同的值会影响局域波的类型、局域波之间相互作用的距离以及局域波的传播方向。所得结果对高阶局域波的研究具有一定的理论参考价值。On the basis of the generalized Darboux transformation,the localized wave solutions of the three-component coupled Kundu-Eckhaus equation were studied and their dynamical characteristics were analyzed.First of all,based on the Darboux matrix and Lax pair of the three-component coupled Kundu-Eckhaus equation,the iterative expression of the localized wave solutions was derived by using the generalized Darboux transformation.Then,according to the classified discussion of the parameters in the expression,the interaction between rogue waves and solitons or breathers was revealed.The evolution diagrams of the first-order and the second-order localized waves were obtained via numerical simulation,and the dynamical characteristics of the localized waves were further analyzed.The results show that different values of the parameters have an influence on the type of localized waves,the distance of interaction between localized waves,and the propagation direction of localized waves.The results obtained have certain theoretical reference value for the study of higher-order localized waves.

关 键 词：耦合Kundu-Eckhaus方程 广义Darboux变换 孤子 局域波 

分 类 号：O241.8[理学—计算数学]