Об интегрируемости деформированной системы Руйсенарса–Шнайдера

Успехи математических наук. 2023. Т. 78. № 2(470). С. 149–188.

Zabrodin A.

We find integrals of motion for the recently introduced
deformed Ruijsenaars–Schneider many-body system, which is the dynami-
cal system for poles of elliptic solutions to the Toda lattice with constraint
of type B. Our method is based on the fact that the equations of motion
for this system coincide with those for pairs of Ruijsenaars–Schneider par-
ticles which stick together preserving a special fixed distance between the
particles. We also obtain B¨acklund transformations and integrable time dis-
cretization of the deformed Ruijsenaars–Schneider system, which is shown
to be the dynamical system for poles of elliptic solutions to the fully discrete
Kadomtsev–Petviashvili equation of type B. In additon, we propose a field
analogue of the deformed Ruijsenaars–Schneider system on a space-time
lattice.

Keywords: интегрируемые системы, integrable systems, дискретное время, Ruijsenaars–Schneider system, integrals of motion, discrete time, интегралы движения, система Руйсенарса–Шнайдера

Publication based on the results of: Representation theory of W-algebras affine and toroidal quantum groups and its applications to geometry, topology and combinatorics (2023)