非线性光纤中耦合非线性薛定谔方程怪波的研究  

Rogue wave of coupled nonlinear schr?dinger equation in the nonlinear optical fibers

作　　者：雷宇祥 宋妮[1] 张毅菲 商慧晶 LEI Yuxiang;SONG Ni;ZHANG Yifei;SHNAG Huijing(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,太原030051

出　　处：《重庆理工大学学报（自然科学）》2022年第3期274-279,共6页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(11602232);山西省自然科学基金项目(201801D221040)。

摘　　要：以描述非线性光纤中电磁波传播的耦合非线性薛定谔方程为研究对象,基于一组特殊形式的种子解,在已有一阶怪波解的基础上,利用广义达布变换及泰勒展式得到了该方程的对称二阶怪波解和非对称二阶怪波解。在一定条件下,选取不同的参数值,研究了参数对怪波动力学性态的影响。通过数值模拟,给出了二阶怪波的等值高线分布图,并对其进行分析,发现二阶怪波具有新的结构,多组波峰呈三角形、中心对称结构分布,所得结果进一步丰富了耦合系统怪波的动力学结构。In this paper, the two-component coupled nonlinear Schr9 dinger equation is taken as the research object, and we take a set of same solutions as seed solutions.On the basis of the first order rogue waves solutions of the coupled nonlinear Schr9 dinger equation, the symmetric second order rogue waves solutions and asymmetric second order rogue waves solutions of the equation were obtained via using the generalized Darboux transformation method and Taylor’s expansion formula.The influence of different parameters on the dynamic behaviors of the rogue waves is studied under certain conditions.By numerical simulation, the contour distribution of the second order rogue waves is given and analyzed.It is found that the second order rogue waves have a new structure, and the peaks of several groups of the rogue waves are triangular and symmetrical in the center.The results further enrich the dynamic structure of the second order rogue waves in the coupled system.

关 键 词：耦合非线性薛定谔方程 广义达布变换 非对称怪波 

分 类 号：O175.29[理学—数学] O437[理学—基础数学]