45 citations · 268 across the 43 of their papers we have counts for
12 papers · 1 filter
Integrable structures of dispersionless systems and differential geometry
Alexander Odesskii
We develop the theory of Whitham type hierarchies integrable by hydrodynamic reductions as a theory of certain differential-geometric objects. As an application we construct Gibbon…
A family of integrable evolution equations of third order
M. Babela, A. Odesskii
We construct a family of integrable equations of the form such that is a transcendental function in . This family is related to the…
Double Poisson brackets on free associative algebras
A. Odesskii, V. Rubtsov, V. Sokolov
We discuss double Poisson structures in sense of M. Van den Bergh on free associative algebras focusing on the case of quadratic Poisson brackets. We establish their relations with…
Non-homogeneous systems of hydrodynamic type possessing Lax representations
A. V. Odesskii, V. V. Sokolov
We consider 1+1 - dimensional non-homogeneous systems of hydrodynamic type that possess Lax representations with movable singularities. We present a construction, which provides a…
Bi-Hamiltonian ODEs with matrix variables
Alexander Odesskii, Vladimir Rubtsov, Vladimir Sokolov
We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an ex…
Integrable (2+1)-dimensional systems of hydrodynamic type
Alexander Odesskii, Vladimir Sokolov
We describe the results that have so far been obtained in the classification problem for integrable (2+1)-dimensional systems of hydrodynamic type. The systems of Gibbons--Tsarev t…