On Generating New $(2+1)$-Dimensional Super Integrable Systems
Received:January 29, 2018  Revised:February 23, 2019
Key Word: Lie super algebra   $(2+1)$-dimensional super equation   Hamiltonian structure  
Fund ProjectL: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).
Author NameAffiliation
Hanyu WEI College of Mathematics and Statistics, Zhoukou Normal University, Henan 466001, P. R. China 
Tiecheng XIA Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China 
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      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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