12 citations · 31 across the 18 of their papers we have counts for
10 papers · 1 filter
Infinite hierarchies of Poisson structures for integrable systems and spectral curves
K. L. Vaninsky
In this short survey, we describe our approach for constructing hierarchies of Poisson brackets for classical integrable systems using its' spectral curves.
The hierarchy of Poisson brackets for the open Toda lattice and its' spectral curves
K. L. Vaninsky
We establish a new representation of the infinite hierarchy of Pois- son brackets (PB) for the open Toda lattice in terms of its spectral curve. For the classical Poisson bracket (…
Analytic Poisson brackets on rational functions on the Riemann sphere and their generalization
K. L. Vaninsky
We consider a hierarchy of Poisson structures defined on rational functions on the Riemann sphere. This hierarchy is originated in the theory of the integrable Camassa-Holm equatio…
A class of nonlinear random walks related to the Ornstein-Uhlenbeck process
S. A. Muzychka, K. L. Vaninsky
Contrary to the theory of Markov processes, no general theory exists for the so called nonlinear Markov processes. We study an example of "nonlinear Markov process" related to clas…
The Atiyah--Hitchin bracket for the cubic Nonlinear Schrodinger equation. IV. the scattering potentials
K. L. Vaninsky
This is the last in a series of four papers on Poisson formalism for the cubic nonlinear Schrodinger equation with repulsive nonlinearity. In this paper we consider scattering pote…
The family of analytic Poisson brackets for the Camassa--Holm hierarchy
M. I. Gekhtman, K. L. Vaninsky
We consider the integrable Camassa--Holm hierarchy on the line with positive initial data rapidly decaying at infinity. It is known that flows of the hierarchy can be formulated in…