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KdV ’95 pp 277-294 | Cite as

A KdV Equation in 2 + 1 Dimensions: Painlevé Analysis, Solutions and Similarity Reductions

  • P. G. Estévez
  • S. B. Leble

Abstract

The nonlinear equation m ty = (m yxx +m x m y ) x is throughly analyzed. The Painlevé test yields a positive result. The Bäcklund transformations are found and the Darboux—Moutard—Matveev formalism arises in the context of this analysis. Some solutions and their interactions are also analyzed. The singular manifold equations are also used to determine symmetry reductions. This procedure can be related with the direct method of Clarkson and Kruskal.

Key words

Painlevé analysis Bäcklund transformation Kadomtsev-Petviashvili equation singular manifold methods 

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • P. G. Estévez
    • 1
  • S. B. Leble
    • 2
  1. 1.Area de Física Teórica, Facultad de CienciasUniversidad de SalamancaSalamancaSpain
  2. 2.Theoretical Physics DepartmentKaliningrad State UniversityKaliningradRussia

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