270 citations · 816 across the 22 of their papers we have counts for
20 papers
Quasi-periodic solutions of the universal hierarchy
I. Krichever, A. Zabrodin
We construct quasi-periodic solutions of the universal hierarchy which includes the multi-component KP and Toda hierarchies and show how they fit into the bilinear formalism. The t…
Quasi-periodic solutions to hierarchies of nonlinear integrable equations and bilinear relations
A. Zabrodin
This is a short review of the construction of quasi-periodic (algebraic-geometrical) solutions to hierarchies of nonlinear integrable equations. As is well known, the solutions are…
Tau-function of the B-Toda hierarchy
V. Prokofev, A. Zabrodin
We continue the study of the B-Toda hierarchy (the Toda lattice with the constraint of type B) which can be regarded as a discretization of the BKP hierarchy. We introduce the tau-…
Elliptic solutions of the Toda lattice with constraint of type B and deformed Ruijsenaars-Schneider system
V. Prokofev, A. Zabrodin
We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by…
Time discretization of the deformed Ruijsenaars-Schneider system
A. Zabrodin
We obtain Bäcklund transformations and integrable time discretization of the recently introduced deformed Ruijsenaars-Schneider many-body system which is the dynamical system for p…
Dyson diffusion on a curved contour
A. Zabrodin
We define the Dyson diffusion process on a curved smooth closed contour in the plane and derive the Fokker-Planck equation for probability density. Its stationary solution is shown…