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Symmetry Groups of Multidimensional Integrable Nonlinear Systems

  • P. Winternitz
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 25)

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.

Keywords

Conjugacy Class Symmetry Algebra Symmetry Reduction Partial Differential System Group Invariant Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • P. Winternitz
    • 1
  1. 1.Centre de Recherches MathématiquesUniversité de MontréalMontréalCanada

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