中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50202-050202.doi: 10.1088/1674-1056/19/5/050202

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A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

王友法1, 钱贤民1, 楼森岳2   

  1. (1)Department of Physics, Ningbo University, Ningbo 315211, China;Department of Physics, Shaoxing University, Shaoxing 312000, China; (2)Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China;School of Mathematics, Fudan University, Shanghai 200433, China
  • 收稿日期:2009-07-27 修回日期:2009-11-23 出版日期:2010-05-15 发布日期:2010-05-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No.~10735030), the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No.~20040969), the National Basic Research Programs of China (Grant Nos.~2007CB814800 and 2005CB422301) and the PCSIRT (IRT0734).

A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

Wang You-Fa(王友法)a)b), Lou Sen-Yue(楼森岳) a)c)d)†, and Qian Xian-Min(钱贤民)b)   

  1. a Department of Physics, Ningbo University, Ningbo 315211, Chinab Department of Physics, Shaoxing University, Shaoxing 312000, China; c Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, Chinad School of Mathematics, Fudan University, Shanghai 200433, China
  • Received:2009-07-27 Revised:2009-11-23 Online:2010-05-15 Published:2010-05-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No.~10735030), the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No.~20040969), the National Basic Research Programs of China (Grant Nos.~2007CB814800 and 2005CB422301) and the PCSIRT (IRT0734).

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摘要： According to the conjecture based on some known facts of integrable models, a new (2+1)-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known (2+1)-dimensional negative Kadomtsev--Petviashvili equation but also the extension of the known (1+1)-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.

Abstract: According to the conjecture based on some known facts of integrable models, a new (2+1)-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known (2+1)-dimensional negative Kadomtsev--Petviashvili equation but also the extension of the known (1+1)-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.

Key words: integrable models, supersymmetry, symmetries and symmetry reductions, exact solutions

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Ik (Integrable systems) 02.30.Tb (Operator theory)