| On Generating New $(2+1)$-Dimensional Super Integrable Systems |
| Received:January 29, 2018 Revised:February 23, 2019 |
| Key Words:
Lie super algebra $(2+1)$-dimensional super equation Hamiltonian structure
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11547175) and the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China (Grant No.2017GGJS145). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.03.007 |
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