108 citations · 390 across the 39 of their papers we have counts for
40 papers
Non-Abelian evolution systems with conservation laws
V. E. Adler, V. V. Sokolov
We find noncommutative analogs for well-known polynomial evolution systems with higher conservation laws and symmetries. The integrability of obtained non-Abelian systems is justif…
Nonabelian elliptic Poisson structures on projective spaces
A. Odesskii, V. Sokolov
We review nonabelian Poisson structures on affine and projective spaces over . We also construct a class of examples of nonabelian Poisson structures on $\mathbb{C} P^{…
Multi-component generalizations of mKdV equation and non-associative algebraic structures
Ivan P. Shestakov, Vladimir V. Sokolov
Relations between triple Jordan systems and integrable multi-component models of the modified Korteveg--de Vries type are established. The most general model is related to a pair c…
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…
The symmetry approach to integrability: recent advances
Rafael Hernández Heredero, Vladimir Sokolov
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recur…
Integrable non-abelization of the flow on an elliptic curve
V. Sokolov, T. Wolf
An integrable non-abelian generalization of a Hamiltonian flow on an elliptic curve is presented. A Lax pair for this non-abelian system is found.