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Integrable anisotropic evolution equations on a sphere. (English) Zbl 1099.35139
Summary: 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.

##### MSC:
 35Q58 Other completely integrable PDE (MSC2000) 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 35L65 Hyperbolic conservation laws
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