128 citations · 447 across the 39 of their papers we have counts for
4 papers · 1 filter
Frolicher structures, diffieties, and a formal KP hierarchy
Jean-Pierre Magnot, Enrique G. Reyes, Vladimir Rubtsov
We propose a definition of a diffiety based on the theory of Frolicher structures. As a consequence, we obtain a natural Vinogradov sequence and, under the assumption of the existe…
On Zakharov-Shabat equations of generalized Kadomtsev-Petviashvili hierarchies
Jean-Pierre Magnot, Enrique G. Reyes, Vladimir Rubtsov
We review the integration of the KP hierarchy in several non-standard contexts. Specifically, we consider KP in the following associative differential algebras: an algebra equipped…
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…
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…