| 魏含玉,夏铁成.新(2+1)-维超可积系统的生成[J].数学研究及应用,2019,39(3):277~288 |
| 新(2+1)-维超可积系统的生成 |
| On Generating New $(2+1)$-Dimensional Super Integrable Systems |
| 投稿时间：2018-01-29 修订日期：2019-02-23 |
| DOI：10.3770/j.issn:2095-2651.2019.03.007 |
| 中文关键词: Lie超代数 (2+1)-维超方程 Hamilton结构 |
| 英文关键词:Lie super algebra $(2+1)$-dimensional super equation Hamiltonian structure |
| 基金项目:国家自然科学基金(Grant No.11547175),河南省高等学校青年骨干教师培养计划资助(Grant No.2017GGJS145). |
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| 中文摘要: |
| 本文利用二项式残数表示方法生成(2+1)-维超可积系统. 由这些系统得到了一个新的(2+1)-维超孤子族，它能约化为(2+1)-维超非线性Schrodinger方程. 特别地,我们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)-维的扩散方程. 最后借助超迹恒等式给出了新(2+1)-维超可积系统的Hamilton结构. |
| 英文摘要: |
| In this paper, we make use of the binormial-residue-representation (BRR) to generate $(2+1)$-dimensional super integrable systems. By using these systems, a new $(2+1)$-dimensional super soliton hierarchy is deduced, which can be reduced to a $(2+1)$-dimensional super nonlinear Schr\"{o}dinger equation. Especially, two main results are obtained which have important physics applications, one of them is a set of $(2+1)$-dimensional super integrable couplings, the other one is a $(2+1)$-dimensional diffusion equation. Finally, the Hamiltonian structure for the new $(2+1)$-dimensional super hierarchy is produced with the aid of the super trace identity. |
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