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2007•Europhysics Letters (EPL)Requires access

Asymptotic symmetries and integrability: The KdV case

D. Levi, Miguel A. Rodrı́guez

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Abstract

In this letter we consider asymptotic symmetries of the Korteweg de Vries equation, the prototype of the integrable equations. While the reduction of the KdV with respect to point and generalized symmetries gives equations of the Painlevé classification, we show here that the reduction with respect to some asymptotic symmetries violates the Ablowitz-Ramani-Segur conjecture and gives an ordinary differential equation which does not possess the Painlevé property.

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What this paper is about

In this letter we consider asymptotic symmetries of the Korteweg de Vries equation, the prototype of the integrable equations. While the reduction of the KdV with respect to point and generalized symmetries gives equations of the Painlevé classification, we show here that the reduction with respect to some asymptotic symmetries violates the Ablowitz-Ramani-Segur conjecture and gives an ordinary differential equation which does not possess the Painlevé property.

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Available abstract

In this letter we consider asymptotic symmetries of the Korteweg de Vries equation, the prototype of the integrable equations. While the reduction of the KdV with respect to point and generalized symmetries gives equations of the Painlevé classification, we show here that the reduction with respect to some asymptotic symmetries violates the Ablowitz-Ramani-Segur conjecture and gives an ordinary differential equation which does not possess the Painlevé property.

Key concepts: Korteweg–de Vries equation, Homogeneous space, Integrable system, Mathematics, Ordinary differential equation, Conjecture, Reduction (mathematics), Mathematical physics

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