中国物理B ›› 2005, Vol. 14 ›› Issue (8): 1486-1494.doi: 10.1088/1009-1963/14/8/002

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Painlevé property, symmetries and symmetry reductions of the coupled Burgers system

连增菊1, 楼森岳2, 陈黎丽3   

  1. (1)Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China; (2)Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China ;Department of Physics, Shanghai Jiaotong University,Shanghai 200030, China; (3)Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China ;Department of Physics, Shanghai Jiaotong University,Shanghai 200030, China
  • 收稿日期:2004-12-19 修回日期:2005-12-27 出版日期:2005-07-13 发布日期:2005-07-13
  • 基金资助:
    Project supported by the National Natural Science Foundations of China (Grant Nos 90203001 and 10475055) and the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No 20040969).

Painlevé property, symmetries and symmetry reductions of the coupled Burgers system

Lian Zeng-Ju (连增菊)a, Chen Li-Li (陈黎丽)ac, Lou Sen-Yue (楼森岳)ab    

  1. a Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China; b Department of Physics, Shanghai Jiaotong University,Shanghai 200030, China; c State Key Laboratory of Modern Acoustics, Nanjing University, Nanjing 210093, China
  • Received:2004-12-19 Revised:2005-12-27 Online:2005-07-13 Published:2005-07-13
  • Supported by:
    Project supported by the National Natural Science Foundations of China (Grant Nos 90203001 and 10475055) and the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No 20040969).

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摘要： The Painlev\'e property, inverse recursion operator,infinite number of symmetries and Lie symmetry reductions of the coupled Burgers equation are given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and the inverse recursion operator on the trivial symmetries such as the identity transformation, the space translation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra while its finite dimensional Lie point symmetry subalgebra is used to find possible symmetry reductions and then the group invariant solutions.

关键词: symmetry, recursion operator, symmetry reduction, Painlevé

Abstract: The Painlev\'e property, inverse recursion operator,infinite number of symmetries and Lie symmetry reductions of the coupled Burgers equation are given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and the inverse recursion operator on the trivial symmetries such as the identity transformation, the space translation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra while its finite dimensional Lie point symmetry subalgebra is used to find possible symmetry reductions and then the group invariant solutions.

Key words: symmetry, recursion operator, symmetry reduction, Painlevé

中图分类号:  (Integrable systems)

  • 02.30.Ik
02.20.Sv (Lie algebras of Lie groups)