Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-15T06:39:17.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Bäcklund transformations from painlevé analysis

Published online by Cambridge University Press:  19 July 2002

Robert Conte  and
Micheline Musette
Robert Conte
Affiliation:
Service de physique de l'état condensé, CEA Saclay, F–91191 Gif-sur-Yvette Cedex, France e-mail: conte@drecam.saclay.cea.fr
Micheline Musette
Affiliation:
Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, B–1050 Brussel, België e-mail: mmusette@vub.ac.be
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Since its elaboration in 1983 by Weiss, Tabor and Carnevale, the method to explicitly build the Bäcklund transformation of a partial differential equation (PDE) from singularity analysis only has been improved in several complementary directions, and at the present time it succeeds for practically all PDEs in 1+1-dimensions. The current state of the art is presented, and the emphasis is put on understanding the method. There are two important stages: first, the definition (identified with a Darboux transformation) of a resummation variable to make the Laurent series a finite one as requested by the definition of the word integrability; second, the link (identified with a linearizing formula to be taken from the classification of Painlevé and Gambier) between this resummation variable and the Lax pair to be found.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue A , June 2001 , pp. 9 - 21
Copyright
© 2001 Glasgow Mathematical Journal Trust