Related papers: The Lax pair for C_2-type Ruijsenaars-Schneider mo…
We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with…
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates appear as the poles of the properly normalised eigenvector…
We derive the Lax connection of the free fermion model on a lattice starting from the fermionic formulation of Bazhanov-Stroganov's three-parameter elliptic parametrization for the R-operator. It results in the Yang-Baxter and decorated…
Using the theory of self-adjoint extensions, we study the relativistic spectral properties of the Landau operator with $\delta$ and $\delta '$ interactions on a cylinder of radius $R$ for a charged spin particle system, formally given by…
Hamiltonian reduction is used to project a trivially integrable system on the Heisenberg double of $SU(n,n)$, to obtain a system of Ruijsenaars type on a suitable quotient space. This system possesses $BC_n$ symmetry and is shown to be…
A dressing method is applied to a matrix Lax pair for the Camassa-Holm equation, thereby allowing for the construction of several global solutions of the system. In particular solutions of system of soliton and cuspon type are constructed…
We present a derivation of the dynamical r-matrices of the Calogero-Moser models using the Hamiltonian reduction procedure to get general formulae. We describe the dynamical r-matrices thus found for spin Calogero-Moser models and…
We propose new types of integrable spinor models, generalizing the well known ones of: i) Nambu-Jona-Lasinio-Vaks-Larkin models, related to SU(N); ii) the Gross-Neveu models - SP(2N); and the iii) Zakharov-Mikhailov models - SO(N). We…
The non-holonomic deformations of non-local integrable systems belonging to the Nonlinear Schrodinger family are studied using the Bi-Hamiltonian formalism as well as the Lax pair method. The non-local equations are first obtained by…
In this paper we study factorization formulae for the Lax matrices of the classical Ruijsenaars-Schneider and Calogero-Moser models. We review the already known results and discuss their possible origins. The first origin comes from the…
We describe classical top-like integrable systems arising from the quantum exchange relations and corresponding Sklyanin algebras. The Lax operator is expressed in terms of the quantum non-dynamical $R$-matrix even at the classical level,…
The Ruijsenaars-Schneider systems are `discrete' version of the Calogero-Moser (C-M) systems in the sense that the momentum operator p appears in the Hamiltonians as a polynomial in e^{\pm\beta' p} (\beta' is a deformation parameter)…
We analyze the integrability of the ${\cal N}$-extended supersymmetric Calogero-Moser model. We explicitly construct the Lax pair $\{L,A\}$ for this system, which properly reproduces all equations of motion. After adding a supersymmetric…
We give an update on our ongoing investigations of potentials between pairs of static-light mesons in Nf=2 Lattice QCD, in different spin and isospin channels. The question of attraction and repulsion is particularly interesting with…
We examine the Hamiltonian structures of some Calogero-Moser and Ruijsenaars-Schneider N-body integrable models. We propose explicit formulations of the bihamiltonian structures for the discrete models, and field-theoretical realizations of…
We outline an approach to a theory of various generalizations of the elliptic Calogero-Moser (CM) and Ruijsenaars-Shneider (RS) systems based on a special inverse problem for linear operators with elliptic coefficients. Hamiltonian theory…
In this paper, we construct a Lax pair for the classical hyperbolic van Diejen system with two independent coupling parameters. Built upon this construction, we show that the dynamics can be solved by a projection method, which in turn…
We consider (3+1)-dimensional second-order evolutionary PDEs where the unknown $u$ enters only in the form of the 2nd-order partial derivatives. For such equations which possess a Lagrangian, we show that all of them have a symplectic…
The classical (dynamical) $R$-matrices for the 2- and 3-body Calogero-Moser models with elliptic potentials are given. The 3-body case has an interesting nontrivial structure that goes beyond the known ansatz for momentum independent…
We present a very simple form of the supercharges and the Hamiltonian of ${\cal N} {=}\,2$ supersymmetric extension of $n$-particle Ruijsenaars--Schneider models for three cases of the interaction: $1/(x_i-x_j)$, $1/tan(x_i-x_j)$,…