| Issue |
EPL
Volume 80, Number 6, December 2007
|
|
|---|---|---|
| Article Number | 60005 | |
| Number of page(s) | 4 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/80/60005 | |
| Published online | 08 November 2007 | |
Asymptotic symmetries and integrability: The KdV case
1
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
Corresponding authors: levi@roma3.infn.it rodrigue@fis.ucm.es
Received:
18
May
2007
Accepted:
17
October
2007
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
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