二分量KN系统三阶流方程的达布变换及其解  

Darboux transformation and its solution for the third-order flow equation of two-component KN system

作　　者：周华鑫 虞静[1] ZHOU Huaxin;YU Jing(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2022年第6期95-99,共5页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(61771174)。

摘　　要：从二分量Kaup-Newell(KN)系统的谱问题出发,运用谱问题空间部分和时间部分的相容性条件(即零曲率方程),得到二分量KN系统的三阶流方程;然后,研究了该三阶流方程的达布变换的构造,并得到变换后的解的表示;最后,从零种子解出发,得到二分量KN系统的三阶流方程的孤子解,并借助Maple软件得出孤子解的三维动力演化图和密度图。By making use of the compatible condition of the spatial and temporal part of the spectral problems, we obtain the third-order flow equations of the two-component Kaup-Newell system. Then we construct the representations of the Darboux transformation and transformed solutions of the equations. As a special example, starting from a zero seed solution, we derive some soliton solutions of the third-order flow equations of the two-component Kaup-Newell system;meanwhile, their three-dimensional and density images are depicted by the Maple software.

关 键 词：二分量Kaup-Newell系统 零曲率方程 达布变换 孤子解 

分 类 号：O29[理学—应用数学]