Related papers: C^{(2)}_{N+1} Ruijsenaars-Schneider models
The Lie-Poisson algebra so(N+1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the ND spherical, Euclidean, hyperbolic, Minkowskian and (anti-)de Sitter spaces. We firstly present a…
D-dimensional constrained systems are studied with stochastic Lagrangian and\break Hamiltonian. It is shown that stochastic consistency conditions are second class constraints and Lagrange multiplier fields can be determined in…
It is shown that the elliptic Ruijsenaars-Schneider model can be obtained from the affine Heisenberg Double by means of the Poisson reduction procedure. The dynamical $r$-matrix naturally appears in the construction.
Given a compact space X and two commuting continuous open surjective maps sigma_1, sigma_2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N^2-action. When the maps sigma_1, sigma_2 are local homeomorphisms,…
We study the Lagrange formalism of the (rational) Ruijsenaars-Schneider (RS) system, both in discrete time as well as in continuous time, as a further example of a Lagrange 1-form structure in the sense of the recent paper [24]. The…
In the paper Lax pairs for linear Hamiltonian systems of differential equations are constructed. In particular, Gr\"obner bases are used for the computations. It is proved that the maps which appear in the construction of Lax pairs are…
We show how the Newton-Hooke (NH) symmetries, representing a nonrelativistic version of de-Sitter symmetries, can be enlarged by a pair of translation vectors describing in Galilean limit the class of accelerations linear in time. We study…
Given a Lax system of equations with the spectral parameter on a Riemann surface we construct a projective unitary representation of the Lie algebra of Hamiltonian vector fields by Knizhnik-Zamolodchikov operators. This provides a…
The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84-117] are extended over consideration of central extensions allowing the introducing of additional independent variables. Algebraic conditions…
We seek to clarify some of the physical aspects of the Ruijsenaars-Schneider models. This important class of models was presented as a relativistic generalisation of the Calogero-Moser models but, as we shall argue, this description is…
Brief review of the methods for solving the multicomponent nonlinear Schrodinger (MNLS) equations and analysis of their Hamiltonian structures is given. Main attention is paid to the MNLS related to the C.II- and D.III-types symmetric…
We propose a new reduction mechanism which allows one to construct n-particle (super)conformal theories with pairwise interaction starting from a composite system involving n(n-1)/2+1 copies of the ordinary (super)conformal mechanics.…
We study multiplicative quiver varieties associated to specific extensions of cyclic quivers with $m\geq 2$ vertices. Their global Poisson structure is characterised by quasi-Hamiltonian algebras related to these quivers, which were studied…
All Lie bialgebra structures for the (1+1)-dimensional centrally extended Schrodinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family…
We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the…
We present generalizations of the well-known trigonometric spin Sutherland models, which were derived by Hamiltonian reduction of `free motion' on cotangent bundles of compact simple Lie groups based on the conjugation action. Our models…
We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N=2 superfield…
The reduction of the quasi-Hamiltonian double of ${\mathrm{SU}}(n)$ that has been shown to underlie Ruijsenaars' compactified trigonometric $n$-body system is studied in its natural generality. The constraints contain a parameter $y$,…
This paper develops a construction of families of $ U(1)^{n-2} $-invariant special Lagrangian $ n $-folds in $ \mathbb{C}^{n} $, extending the analytic framework introduced by Joyce ($ n = 3 $) to arbitrary dimension. By reducing the…
We consider one-dimensional elliptic Ruijsenaars model of type $BC_1$. It is given by a three-term difference Schr\"odinger operator $L$ containing 8 coupling constants. We show that when all coupling constants are integers, $L$ has…