Communications in Mathematical Physics

, Volume 232, Issue 1, pp 1–18 | Cite as

Integrable Evolution Equations on the N-Dimensional Sphere

  • A.G. Meshkov
  • V.V. Sokolov

Abstract:

 The problem of a classification of integrable evolution equations on the\break N-dimensional sphere is considered. We modify the main notions of the symmetry approach such as the formal symmetry and the canonical series of conserved densities to the case of such equations. Using these theoretical results, we solve several special classification problems. The main result is a complete classification of integrable isotropic evolution equations of third order on the sphere. An important class of anisotropic equations is also considered.

Keywords

Theoretical Result Evolution Equation Classification Problem Important Class Special Classification 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • A.G. Meshkov
    • 1
  • V.V. Sokolov
    • 2
  1. 1.Orel State University, Komsomolskaya str., 95, 302026 Orel, RussiaRU
  2. 2.Landau Institute for Theoretical Physics, Kosygina str. 2, 117334 Moscow, RussiaRU

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