中国物理B ›› 2007, Vol. 16 ›› Issue (2): 303-309.doi: 10.1088/1009-1963/16/2/006

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Lie symmetry analysis and reduction of a new integrable coupled KdV system

钱素平1, 田立新2   

  1. (1)Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China;Nonlinear Scientific Research Center, Faculty of Science,Jiangsu University, Zhenjiang 212013, China; (2)Nonlinear Scientific Research Center, Faculty of Science,Jiangsu University, Zhenjiang 212013, China
  • 收稿日期:2006-05-31 修回日期:2006-06-26 出版日期:2007-02-20 发布日期:2007-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10071033), the Natural Science Foundation of Jiangsu Province, China (Grant No BK2002003), and the Technology Innovation Plan for Postgraduate of Jiangsu Province in 2006 (Grant No 72).

Lie symmetry analysis and reduction of a new integrable coupled KdV system

Qian Su-Ping(钱素平)a)b)† and Tian Li-Xin(田立新)b)   

  1. a Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China; b Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, China
  • Received:2006-05-31 Revised:2006-06-26 Online:2007-02-20 Published:2007-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10071033), the Natural Science Foundation of Jiangsu Province, China (Grant No BK2002003), and the Technology Innovation Plan for Postgraduate of Jiangsu Province in 2006 (Grant No 72).

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摘要： In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg--de Vries (KdV) equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invariant solution of reduced equations can be acquired by means of the Painlev\'e I transcendent function.

关键词: the coupled KdV equations, symmetry reduction, group-invariant solutions

Abstract: In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg--de Vries (KdV) equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invariant solution of reduced equations can be acquired by means of the Painlevé I transcendent function.

Key words: the coupled KdV equations, symmetry reduction, group-invariant solutions

中图分类号:  (Lie algebras of Lie groups)

  • 02.20.Sv
02.30.Jr (Partial differential equations)