EPL, 80 (2007) 60005
DOI: 10.1209/0295-5075/80/60005

Asymptotic symmetries and integrability: The KdV case

D. Levi¹ and M. A. Rodríguez<sup>2

1</sup>  Dipartimento di Ingegneria Elettronica, Università Roma Tre and INFN-Sezione di Roma Tre Via della Vasca Navale 84, I-00146 Roma, Italy
²  Departamento de Física Teórica II, Universidad Complutense - E-28040 Madrid, Spain

levi@roma3.infn.it
rodrigue@fis.ucm.es

received 18 May 2007; accepted in final form 17 October 2007; published December 2007
published online 8 November 2007

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.

PACS
02.30.Ik - Integrable systems.
02.20.Sv - Lie algebras of Lie groups.
02.30.Hq - Ordinary differential equations.

© EPLA 2007