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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (3): 355-366.doi: 10.3969/j.issn.1005-3085.2018.03.010

• • 上一篇    

一个新 6 分量超 NLS-MKdV 族的超 Hamilton 结构和守恒律（英）

魏含玉1,   夏铁成2   

  1. 1- 周口师范学院数学与统计学院，周口  466001
    2- 上海大学数学系，上海  200444
  • 收稿日期:2016-08-22 接受日期:2017-06-27 出版日期:2018-06-15 发布日期:2018-08-15
  • 通讯作者: 魏含玉 E-mail: weihanyu8207@163.com
  • 基金资助:
    国家自然科学基金(11547175; 11271008; 11501526)；河南省高等学校骨干青年教师援助项目(2017GGJS145).

Conservation Laws and Super Hamiltonian Structures for a New Six-component Super NLS-MKdV Hierarchy

WEI Han-yu1,   XIA Tie-cheng2   

  1. 1- College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001
    2- Department of Mathematics, Shanghai University, Shanghai 200444
  • Received:2016-08-22 Accepted:2017-06-27 Online:2018-06-15 Published:2018-08-15
  • Contact: H. Wei. E-mail: weihanyu8207@163.com
  • Supported by:
    The National Natural Science Foundation of China (11547175; 11271008; 11501526); the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China (2017GGJS145).

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摘要： 在孤子理论中，如何构造新的超孤子族是个重要的问题．基于矩阵李超代数，我们借助于零曲率方程构造了一个新的六分量超NLS-MKdV族，并给出了超可积方程不同的约化．利用超迹恒等式，我们得到了非线性超可积方程族的超Hamilton结构．最后，通过引入两个变量，我们建立了六分量超可积NLS-MKdV族的无穷守恒律．特别地，费米变量在超可积系统计算过程中起了重要作用．

关键词: 超Hamiltonian结构, 守恒律, 超NLS-MKdV族, Fermi变量

Abstract: How to construct a new super soliton equation hierarchy is an important problem in soliton theory. In this paper, based on the matrix Lie super algebras, we obtain a new six-component super NLS-MKdV hierarchy with the aid of zero curvature equation, and gain different reductions for the super integrable equations. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy. Finally, we establish infinite conservation laws for the integrable six-component super NLS-MKdV hierarchy by introducing two variables. Especially, in the process of computation, Fermi variables play an important role in super integrable systems.

Key words: super Hamiltonian structure, conservation law, super NLS-MKdV hierarchy, Fermi variable

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