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Prolongation structure of the variable coefficient KdV equation |
Yang Yun-Qing(杨云青)a) and Chen Yong(陈勇)a)b)† |
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 |
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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.
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Received: 17 March 2010
Revised: 13 August 2010
Accepted manuscript online:
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PACS:
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02.30.Ik
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(Integrable systems)
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05.45.Yv
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(Solitons)
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Fund: 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. |
Cite this article:
Yang Yun-Qing(杨云青) and Chen Yong(陈勇) Prolongation structure of the variable coefficient KdV equation 2011 Chin. Phys. B 20 010206
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