中国物理B ›› 2011, Vol. 20 ›› Issue (1): 10206-010206.doi: 10.1088/1674-1056/20/1/010206

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Prolongation structure of the variable coefficient KdV equation

杨云青1, 陈勇2   

  1. (1)Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China; (2)Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China
  • 收稿日期:2010-03-17 修回日期:2010-08-13 出版日期:2011-01-15 发布日期:2011-01-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10735030 and 90718041), the Shanghai Leading Academic Discipline Project, China (Grant No. B412), the Program for Changjiang Scholars, the Innovative Research Team in University, Ministry of Education of China (Grant No. IRT 0734) and the K.C.Wong Magna Fund in Ningbo University, China.

Prolongation structure of the variable coefficient KdV equation

Yang Yun-Qing(杨云青)a) and Chen Yong(陈勇)a)b)†   

  1. a Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China; b Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China
  • Received:2010-03-17 Revised:2010-08-13 Online:2011-01-15 Published:2011-01-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10735030 and 90718041), the Shanghai Leading Academic Discipline Project, China (Grant No. B412), the Program for Changjiang Scholars, the Innovative Research Team in University, Ministry of Education of China (Grant No. IRT 0734) and the K.C.Wong Magna Fund in Ningbo University, China.

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摘要： The prolongation structure methodologies of Wahlquist--Estabrook [Wahlquist H D and Estabrook F B 1975 J. Math. Phys. 16 1] for nonlinear differential equations are applied to a variable-coefficient KdV equation. Based on the obtained prolongation structure, a Lie algebra with five parameters is constructed. Under certain conditions, a Lie algebra representation and three kinds of Lax pairs for the variable- coefficient KdV equation are derived.

关键词: prolongation structure, variable-coefficient KdV equation, Lax pairs

Abstract: The prolongation structure methodologies of Wahlquist–Estabrook [Wahlquist H D and Estabrook F B 1975 J. Math. Phys. 16 1] for nonlinear differential equations are applied to a variable-coefficient KdV equation. Based on the obtained prolongation structure, a Lie algebra with five parameters is constructed. Under certain conditions, a Lie algebra representation and three kinds of Lax pairs for the variable- coefficient KdV equation are derived.

Key words: prolongation structure, variable-coefficient KdV equation, Lax pairs

中图分类号:  (Integrable systems)

  • 02.30.Ik
05.45.Yv (Solitons)