26 citations · 71 across the 9 of their papers we have counts for
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Classification of integrable vector equations of geometric type
Anatoly Meshkov, Vladimir Sokolov
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the…
Integrable evolution equations with constant separant
A. G. Meshkov, V. V. Sokolov
The survey provides classification results for integrable one-field evolution equations of orders 2, 3 and 5 with the constant separant. The classification is based on necessary in…
Vector hyperbolic equations on the sphere possessing integrable third order symmetries
Anatoly Meshkov, Vladimir Sokolov
The complete lists of vector hyperbolic equations on the sphere that have integrable third order vector isotropic and anisotropic symmetries are presented. Several new integrable h…
Integrable hyperbolic equations of sin-Gordon type
A. G. Meshkov, V. V. Sokolov
A complete list of nonlinear one-field hyperbolic equations having generalized integrable x- and y-symmetries of the third order is presented. The list includes both sin-Gordon typ…
Nonlocal symmetries of integrable two-field divergent evolutionary systems
A. G. Meshkov
Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial…
Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions
Anatoly G. Meshkov, Maxim Ju. Balakhnev
A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is pro…
Integrable Anisotropic Evolution Equations on a Sphere
Anatoly G. Meshkov, Maxim Ju. Balakhnev
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 classificatio…