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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 ›› 2019, Vol. 36 ›› Issue (6): 708-720.doi: 10.3969/j.issn.1005-3085.2019.06.009

• • 上一篇    下一篇

新(2+1)-维超动力系统的生成（英）

魏含玉1,  张  燕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:2017-07-31 接受日期:2019-06-03 出版日期:2019-12-15 发布日期:2020-02-15
  • 通讯作者: 魏含玉 E-mail address: weihanyu8207@163.com
  • 基金资助:
    国家自然科学基金(11547175)；河南省高等学校骨干青年教师资助项目(2017GGJS145).

Generating New Super Dynamical Systems in (2+1)-dimensional Space

WEI Han-yu1,  ZHANG Yan1,  XIA Tie-cheng2   

  1. 1- College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001
    2- Department of Mathematics, Shanghai University, Shanghai 200444
  • Received:2017-07-31 Accepted:2019-06-03 Online:2019-12-15 Published:2020-02-15
  • Contact: H. Wei. E-mail address: weihanyu8207@163.com
  • Supported by:
    The National Natural Science Foundation of China (11547175); the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education (2017GGJS145).

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摘要： 本文利用二项式残数表示方法生成 (2+1)-维超动力系统，利用这些系统得到一个新的 (2+1)-维超 NLS-MKdV 族，它能约化为超非线性 Schrodinger 方程．特别地得到两个具有重要物理应用的结果，一个是 (2+1)-维超可积耦合方程，另一个是 (2+1)-维扩散方程．最后，利用超迹恒等式给出了新 (2+1)-维超可积系统的超 Hamilton 结构．

关键词: 二项式残数表示方法, Lie 超代数, 超 NLS-MKdV 族, 超 Hamilton 结构

Abstract: In the article, we make use of the binormial-residue-representation (BRR) to generate (2+1)-dimensional super dynamical systems. By using these systems, a new (2+1)-dimensional super NLS-MKdV hierarchy is deduced, which can be reduced to super nonlinear Schrodinger equation. Especially, two main results are obtained which have important physical applications. One of them is a set of (2+1)-dimensional super integrable couplings, the other one is a (2+1)-dimensional diffusion equation. Furthermore, Super trace identity is used to furnish the super Hamiltonian structures for the new (2+1)-dimensional super integrable system.

Key words: binormial-residue-representation method, Lie super algebra, super NLS-MKdV hierarchy, super Hamiltonian structures

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