Related papers: Correspondence between Calogero-Moser systems and …
We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable'…
The integrability of the deformed quantum elliptic Calogero-Moser problem introduced by Chalykh, Feigin and Veselov is proven. Explicit recursive formulae for the integrals are found. For integer values of the parameter this implies the…
We present a general scheme for constructing the Poisson structure of super-integrable dynamical systems of which the rational Calogero-Moser system is one of the most interesting one. This dynamical system is $2N$ dimensional with $2N- 1$…
The 2x2 monodromy matrices for the Kowalewski top on the Lie algebras e(3), so(4) and so(3,1) are presented. The corresponding quadratic R-matrix structure is the dynamical deformation of the standard R-matrix algebras. Some tops and Toda…
We construct several new families of exactly and quasi-exactly solvable BC_N-type Calogero-Sutherland models with internal degrees of freedom. Our approach is based on the introduction of two new families of Dunkl operators of B_N type…
The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of R^n to the `angular Calogero-Moser model' on…
We construct integrable generalizations of the elliptic Calogero-Sutherland-Moser model of particles with spin, involving noncommutative spin interactions. The spin coupling potential is a modular function and, generically, breaks the…
We construct the Runge-Lenz vector and symmetry algebra of rational Calogero-Coulomb problem, formulated in terms of Dunkl operators. We find that they are proper deformations of their Coulomb counterpart. Together with similar…
We investigate the symmetry algebras of integrable spin Calogero systems constructed from Dunkl operators associated to finite Coxeter groups. Based on two explicit examples, we show that the common view of associating one symmetry algebra…
The algebra of observables of an N-body Calogero model is represented on the S_N-symmetric subspace of the positive definite Fock space. We discuss some general properties of the algebra and construct four different realizations of the…
We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system as a particular case. For the general class, we introduce separation…
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 construct the $r$-matrix for the generalization of the Calogero-Moser system introduced by Gibbons and Hermsen. By reduction procedures we obtain the $r$-matrix for the $O(N)$ Euler-Calogero-Moser model and for the standard $A_N$…
We present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through…
Integrability, algebraic structures and orthogonal basis of the Calogero model are studied by the quantum Lax and Dunkl operator formulations. The commutator algebra among operators including conserved operators and creation-annihilation…
We describe a class of the singular solutions to the multicomponent analogs of the Lam{\'e} equation, arising as equations of motion of the elliptic Calogero--Moser systems of particles carrying spin 1/2. At special value of the coupling…
The rings of quantum integrals of the generalized Calogero-Moser systems related to the deformed root systems ${\cal A}_n(m)$ and ${\cal C}_n(m,l)$ with integer multiplicities and corresponding algebras of quasi-invariants are investigated.…
A multiparameter class of integrable systems is introduced.
We show that it is possible to deduce the Calogero-Moser partition of the irreducible representations of the complex reflection groups G(m,d,n) from the corresponding partition for G(m,1,n). This confirms, in the case W = G(m,d,n), a…
A class of inhomogeneous nonlinear Schr\"odinger equations (NLS), claiming to be novel integrable systems with rich properties continues appearing in PhysRev and PRL. All such equations are shown to be not new but equivalent to the standard…