Geodesic
Integrable Anisotropic Evolution Equations on a Sphere
Symmetry, integrability and geometry: methods and applications, Tome 1 (2005) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: evolution equation; equation on a sphere; integrability; symmetry classification; anisotropy; conserved densities; Bäcklund transformations. 
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Anatoly G. Meshkov; Maxim Ju. Balakhnev. Integrable Anisotropic Evolution Equations on a Sphere. Symmetry, integrability and geometry: methods and applications, Tome 1 (2005). http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a26/

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