五阶耦合扩展mKdV方程的N阶孤子解  

Nth order Soliton Solutions of the Fifth-order Coupled Extended mKdV Equation

作　　者：刘亚停 文竹妍 魏周超[2] 宋妮[1] Liu Yating;Wen Zhuyan;Wei Zhouchao;Song Ni(School of Mathematics,North University of China,Taiyuan 030051,China;School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]中北大学数学学院,太原030051 [2]中国地质大学(武汉)数学与物理学院,武汉430074

出　　处：《动力学与控制学报》2024年第9期24-28,共5页Journal of Dynamics and Control

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

摘　　要：基于二分量五阶耦合扩展修正的Korteweg-de Vries(mKdV)方程,借助广义Darboux变换和Taylor展式,得到方程N阶孤子解的迭代表达式.对谱参数的实部和虚部分类讨论,取合适的自由参数,通过数值模拟展示孤子间的相互作用图,进一步分析不同参数对孤子间弹性及非弹性碰撞的影响.所得结果对高阶孤子的研究具有一定的理论意义.Korteweg-de Vries(mKdV)equation modified by two-component five-order coupled extension is proposed.By means of generalized Darboux transformation and Taylor's expansion,the iterative expression of soliton solution of the order of the equation is obtained.After the real and imaginary sectors of the spectrum parameters are discussed,the free parameters are given to appropriate values.The interaction graphs between solitons are drawn by numerical simulation,and the effects of different parameters on the elastic and inelastic collisions between solitons are further analyzed.The obtained results have a certain theoretical significance for the study of higher-order solitons.

关 键 词：广义Darboux变换 LAX对 MKDV方程 孤子解 

分 类 号：O175[理学—数学]