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Symmetry Groups of Multidimensional Integrable Nonlinear Systems

  • Conference paper
Solitons in Physics, Mathematics, and Nonlinear Optics

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 25))

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Abstract

The Lie groups of local point symmetries of such integrable nonlinear multidimensional systems as the Kadomtsev-Petviashvili equation, the Davey-Stewartson equation, the three-wave resonant interaction equations (3WRI) and others are all infinite-dimensional. Their Lie algebras are Kac-Moody-Virasoro algebras. This fact and its uses are illustrated on the example of the 3WRI system and new solutions of the system are found.

Résumé

Les groupes de Lie de transformations ponctuelles locales de systèmes multidimensionnels intégrables non-linéaires, comme l’équation de Kadomtsev-Petviashvili, l’équation de Davey-Stewartson, les équations d’interaction de trois ondes résonantes (3WRI) et d’autres, sont tous de dimension infinie. Leurs algèbres de Lie sont des algèbres de Kac-Moody-Virasoro. Ce résultat et son utilité sont illustrés dans l’exemple du système 3WRI et de nouvelles solutions au système sont trouvées.

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Author information

Authors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, CP 6128-A, Montréal, Québec, H3C 3J7, Canada

    P. Winternitz

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  1. P. Winternitz
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA

    Peter J. Olver  & David H. Sattinger  & 

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© 1990 Springer-Verlag New York Inc.

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Winternitz, P. (1990). Symmetry Groups of Multidimensional Integrable Nonlinear Systems. In: Olver, P.J., Sattinger, D.H. (eds) Solitons in Physics, Mathematics, and Nonlinear Optics. The IMA Volumes in Mathematics and Its Applications, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9033-6_11

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  • DOI: https://doi.org/10.1007/978-1-4613-9033-6_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9035-0

  • Online ISBN: 978-1-4613-9033-6

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