On the completely integrable calogero-type discretizations of Lax-integrable nonlinear dynamical systems and related coadjoint Markov-type orbits

Abstract

The Calogero-type matrix discretization scheme is applied to THE construction of Lax-type integrable discretizations of one sufficiently wide class of nonlinear integrable dynamical systems on functional manifolds. Their Lie-algebraic structure and complete integrability related to the coadjoint orbits on the Markov coalgebras is discussed. It is shown that the set of conservation laws and the associated Poisson structure can be obtained as a byproduct of the proposed approach. Based on the quasirepresentation property of Lie algebras, the limiting procedure of finding nonlinear dynamical systems on the corresponding functional spaces is demonstrated.