耦合Gerdjikov-Ivanov方程高阶孤子解的研究  

Study on High-Order Soliton Solutions of the Coupled Gerdjikov-Ivanov Equation

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

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2022年第2期112-115,128,共5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);山西省研究生创新项目基金(2021Y629)。

摘　　要：基于Lax对方程和Darboux矩阵,利用广义Darboux变换推导了耦合Gerdjikov-Ivanov(cGI)方程高阶孤子解的迭代表达式.根据谱参数的实部和虚部是否相等进行了分类讨论,在选定谱参数的前提下,对方程解表达式中的自由参数进行取值,通过数值模拟得到二阶和三阶孤子相互作用的演化图,分析讨论了cGI方程高阶孤子的动力学特性.所得结果对研究孤子的传播轨迹和能量变化具有一定的参考意义.On the basis of Lax pair equation and Darboux matrix,the iterative expression of higher-order soliton solutions for the coupled Gerdjikov-Ivanov(cGI)equation was derived by using generalized Darboux transformation.According to the classified discussion on whether the real part and imaginary part of the spectral parameters were equal,on the premise of selecting the spectral parameters,the free parameters were taken in the expression of the square solution,and the evolution diagrams of the interaction between the second-order and third-order solitons were obtained via numerical simulation.The dynamic characteristics of the higher-order solitons in the cGI equation were discussed.The results can be referenced by the study of the propagation path and energy variation of solitons.

关 键 词：耦合Gerdjikov-Ivanov方程 经典Darboux变换 广义Darboux变换 孤子解 

分 类 号：O175[理学—数学]