Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 1 (2005), 027, 11 pages      nlin.SI/0512032      http://dx.doi.org/10.3842/SIGMA.2005.027

Integrable Anisotropic Evolution Equations on a Sphere

Anatoly G. Meshkov and Maxim Ju. Balakhnev
Orel State University, 95 Komsomol'skaya Str., Orel, 302026 Russia

Received September 25, 2005, in final form December 09, 2005; Published online December 14, 2005

Abstract
V.V. Sokolov's modifying symmetry approach is applied to anisotropic evolution equations of the third order on the n-dimensional sphere. The main result is a complete classification of such equations. Auto-Bäcklund transformations are also found for all equations.

Key words: evolution equation; equation on a sphere; integrability; symmetry classification; anisotropy; conserved densities; Bäcklund transformations.

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