一个负阶广义AKNS系统  

A negative order generalized AKNS system

作　　者：朱晨迪 康静 闵卓凡 ZHU Chendi;KANG Jing;MIN Zhuofan(School of Mathematics,Northwest University,Xi′an 710127,China;School of Computing Science,University of Glasgow,Glasgow G128QQ,UK)

机构地区：[1]西北大学数学学院,陕西西安710127 [2]格拉斯哥大学计算机科学学院,苏格兰格拉斯哥G128QQ

出　　处：《纯粹数学与应用数学》2024年第4期606-616,共11页Pure and Applied Mathematics

基　　金：国家自然科学基金(12371252).

摘　　要：本文提出了一个与4×4矩阵谱问题相联系的新的负阶广义AKNS方程族.此方程族的典型方程是一个四分量负阶广义AKNS系统.本文给出了此四分量系统的Lax对及其达布变换.利用达布变换,构造出了此四分量负阶广义AKNS系统的孤子解,包括亮孤子解,暗孤子解及其相互作用.In this paper,a new negative order generalized AKNS hierarchy related to a 4×4 matrix spectral problem is proposed.The prototypical equation of this hierarchy is a four-component negative order generalized AKNS system.The Lax pair and Darboux transformation of this four-component system are given.The soliton solutions of this four-component negative order generalized AKNS system are constructed by using Darboux transformation,including bright soliton solutions,dark soliton solutions and their interactions.

关 键 词：负阶AKNS方程 LAX对 达布变换 孤子解 

分 类 号：O175[理学—数学]