We suggest the procedure of the construction of Baxter Q-operators for Toda chain. Apart from the one-paramitric family of Q-operators, considered in our recent paper [4] we also give theâ€¦ (More)

We discuss the construction of Baxter's Q-operator. The suggested approach leads to the one-parametric family of Q-operators, satisfying to the wronslian-type relations. Also we have found theâ€¦ (More)

In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former isâ€¦ (More)

Baxters's Q-operators for the simplest q-deformed model. Abstract In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Laxâ€¦ (More)

We consider the singular configurations of gravitating gas [1] which could be used as a model for disk galaxies. The simplest steady configuration , which corresponds to rotation of stars aroundâ€¦ (More)

Following the procedure, described in the paper [9], for the integrable DST chain we construct Baxter Q-operators [1] as the traces of monodromy of some M-operators, that act in quantum and auxiliaryâ€¦ (More)

The exact solution of the classical torus automorphism, which partial case is Arnold Cat map is obtained and compared with the numerical solution. The torus, considered as the classical phase spaceâ€¦ (More)

In [1] was considered the superintegrable system which describes the magnetic dipole with spin 1 2 (neutron) in the field of linear current. Here we present its generalization for any spin whichâ€¦ (More)

On the Algebraic Bethe Ansatz for XXX spin chain: creation operators " beyond the equator ". Abstract Considering the XXX spin-1/2 chain in the framework of the Algebraic Bethe Ansatz (ABA) we makeâ€¦ (More)