基于李代数sl(m+1,R)的多分量扰动AKNS孤子梯队

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 24-33.

基于李代数sl(m+1,R)的多分量扰动AKNS孤子梯队

狄艳媚¹, 李春霞², 沈守枫¹, 马文秀³

1. 浙江工业大学应用数学系杭州 310023;
2. 首都师范大学数学科学学院北京 100048;
3. 南佛罗里达大学数学和统计学系美国坦帕 FL 33620-5700

收稿日期:2016-12-17 修回日期:2017-06-07 出版日期:2018-02-26 发布日期:2018-02-26
作者简介:狄艳媚,mathymdi@163.com
基金资助:
浙江省教育厅基金（Y201432067）和国家自然科学基金（11371323）

Multicomponent Perturbed AKNS Soliton Hierarchy Associated with the Lie Algebra sl(m + 1, R)

Di Yanmei¹, Li Chunxia², Shen Shoufeng¹, Ma Wenxiu³

1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023;
2. School of Mathematical Sciences, Capital Normal University, Beijing 100048;
3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA

Received:2016-12-17 Revised:2017-06-07 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the Zhejiang Education Department (Y201432067) and the NSFC (11371323)

摘要/Abstract

摘要： 基于李代数sl（m+1，R），提出了一个新的多分量矩阵谱问题，进而利用零曲率公式构造了新的多分量扰动AKNS孤子梯队.利用迹恒等式构造了双哈密顿结构，同时给出了遗传递推算子.

关键词: 矩阵谱问题, 扰动AKNS孤子梯队, 双哈密顿结构, 递推算子, sl (m+1, R)

Abstract: A new multicomponent matrix spectral problem associated with the Lie algebra sl(m+1,R) is proposed, and new perturbed AKNS soliton hierarchy is generated by the corresponding zero curvature formulation. By virtue of the trace identity, a bi-Hamiltonian structure is established for the hierarchy, and a common hereditary recursion operator is explicitly worked out.

Key words: Matrix spectral problem, Perturbed AKNS soliton hierarchy, Bi-Hamiltonian structure, Recursion operator, sl (m+1,R)

中图分类号:

狄艳媚, 李春霞, 沈守枫, 马文秀. 基于李代数sl(m+1,R)的多分量扰动AKNS孤子梯队[J]. 数学物理学报, 2018, 38(1): 24-33.

Di Yanmei, Li Chunxia, Shen Shoufeng, Ma Wenxiu. Multicomponent Perturbed AKNS Soliton Hierarchy Associated with the Lie Algebra sl(m + 1, R)[J]. Acta mathematica scientia,Series A, 2018, 38(1): 24-33.

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