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SIGMA 1 (2005), 027, 11 pages nlin.SI/0512032
https://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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