Prolongation structure of the variable coefficient KdV equation |
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| Authors: | Yang Yun-Qing and Chen Yong |
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| Institution: | 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 |
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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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| Keywords: | prolongation structure variable-coefficient KdV equation Lax pairs |
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