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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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| [1] |
Wahlquist H D and Estabrook F B 1975 J. Math. Phys. 16 1
|
| [2] |
Cartan acuteE 1945 Les systgraveemes diffacuteerentials extacuteerieurs et leurs applications gacuteeomacuteetriques (Pairs: Hermann)
|
| [3] |
Hermann R 1976 Phys. Rev. Lett. 36 835
|
| [4] |
Dodd R K and Fordy A P 1983 Proc. R. Soc. Lond. A 385 389
|
| [5] |
Dodd R K and Fordy A P 1984 J. Phys. A: Math Gen 17 3249
|
| [6] |
Harrison B K 1983 Lecture Notes in Phys. 205 26
|
| [7] |
Estabrook F B Lecture Notes in Math. 515 136
|
| [8] |
Grimshaw R 1979 Proc. R. Soc. Lond. A 368 359
|
| [9] |
Nirmala N, Vedan M J and Baby B V 1986 J. Math. Phys. 27 2640
|
| [10] |
Lou S Y and Ruan H Y 1992 Acta Phys. Sin. 41 182 (in Chinese)
|
| [11] |
Fan E G 1998 Acta Phys. Sin. (Overseas Edition) 7 649 (in Chinese)
|
| [12] |
Chen Y 2005 NUOVO CIMENTO B 120 295
|
| [13] |
Weiss J, Tabor M and Carnevale G 1983 J. Math. Phys. 24 522
|
| [14] |
Mao J J and Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese)
|
| [15] |
Yan Z Y and Zhang H Q 1999 Acta Phys. Sin. (Overseas Edition) 8 889
|
| [16] |
Tang X Y, Gao Y, Huang F and Lou S Y 2009 Chin. Phys. B 18 4622
|
| [17] |
Joshi N 1987 Phys. Lett. A 125 456
|
| [19] |
Harrison B K 2000 Proceedings of Institute of Mathematics of NAS of Ukraine 30 17
|
| [18] |
Weiss J 1983 J. Math. Phys. 24 1405
|
| [20] |
Nucci M C 1988 J. Phys. A: Math. Gen. 21 73
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