相关论文: Structures in BC_N Ruijsenaars-Schneider models

Drinfeld defined a unitarized R-matrix for any quantum group U_q(g). This gives a commutor for the category of U_q(g) representations, making it into a coboundary category. Henriques and Kamnitzer defined another commutor which also gives…

A kind of Bargmann symmetry constraints involving Lax pairs and adjoint Lax pairs is proposed for soliton hierarchy. The Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative finite dimensional integrable…

We employ a Lax pair representation of the two-component BKP hierarchy and construct its bihamiltonian structure with R-matrix techniques.

We study a holomorphic Poisson structure defined on the linear space $S(n,d):= {\rm Mat}_{n\times d}(\mathbb{C}) \times {\rm Mat}_{d\times n}(\mathbb{C})$ that is covariant under the natural left actions of the standard ${\rm…

A complete description of the non-dynamical r-matrices of the degenerate Calogero-Moser models based on $gl_n$ is presented. First the most general momentum independent r-matrices are given for the standard Lax representation of these…

Ruijsenaars-Schneider models associated with $A_{n-1}$ root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic" limit, we…

We study the differential and Riemannian geometry of algebras $A$ endowed with an action of a triangular Hopf algebra $H$ and noncommutativity compatible with the associated braiding. The modules of one forms and of braided derivations are…

We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of $W_n$…

A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients required for the…

We study a single matrix oscillator with the quadratic Hamiltonian and deformed commutation relations. It is equivalent to the multispecies Calogero model in one dimension, with inverse-square two-body and three-body interactions.…

For the Hamiltonian integrable systems governed by SL(2)-invariant r-matrix (such as Heisenberg magnet, Toda lattice, nonlinear Schroedinger equation) a general procedure for constructing Baecklund transformation is proposed. The…

We construct two series of commuting Hamiltonians parametrized by a constant matrix. The first series was my guess and the second one was know, and in our approach follows from the first series. For the proof we use familier facts known…

It is shown that if a non-autonomous system of $2n$ first-order ordinary differential equations is expressed in the form of the Hamilton equations in terms of two different sets of coordinates, $(q_{i}, p_{i})$ and $(Q_{i}, P_{i})$, then…

The most general momentum independent dynamical r-matrices are described for the standard Lax representation of the degenerate Calogero-Moser models based on $gl_n$ and those r-matrices whose dynamical dependence can be gauged away are…

The representations of the Schr\"odinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable…

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…

This paper showed that Poisson brackets in quaternion variables can be obtained directly from canonical Poisson brackets on cotangent bundle of $SE(3)$ (or $SO(3)$) endowed by canonical symplectic geometry. Quaternion parameters in our case…

Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…

In this paper, we investigate the scattering properties of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-van Diejen many-particle systems with three independent coupling constants. Utilizing the recently…

We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained. All our examples possess dispersionless…