相关论文: r-matrices for relativistic deformations of integr…

A generalization of the notion of a (pseudo-) Riemannian space is proposed in a framework of noncommutative geometry. In particular, there are parametrized families of generalized Riemannian spaces which are deformations of classical…

The $r$-KdV-CH hierarchy is a generalization of the Korteweg-de Vries and Camassa-Holm hierarchies parametrized by $r+1$ constants. In this paper we clarify some properties of its multi-Hamiltonian structures, prove the semisimplicity of…

Recently, relative Rota-Baxter (Lie/associative) algebras are extensively studied in the literature from cohomological points of view. In this paper, we consider relative Rota-Baxter Leibniz algebras (rRB Leibniz algebras) as the object of…

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

Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…

We introduce integrable multicomponent non-commutative lattice systems, which can be considered as analogs of the modified Gel'fand-Dikii hierarchy. We present the corresponding systems of Lax pairs and we show directly multidimensional…

The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to…

We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential.…

N-site-lattice Hamiltonians H are introduced and perceived as a set of systematic discrete approximants of a certain PT-symmetric square-well-potential model with the real spectrum and with a non-Hermiticity which is localized near the…

In the simplest model of horizontal U(1) symmetry with one singlet added to the supersymmetric standard model, we systematically reconstruct quark mass matrices from the low-energy data to prove that there are only two mass matrices found…

A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of $\delta$-pseudo-differential operators, valid on an arbitrary regular time scale, is…

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 translate effectively our earlier quantum constructions to the classical language and using Yang-Baxterisation of the Faddeev-Reshetikhin-Takhtajan algebra are able to construct Lax operators and associated $r$-matrices of classical…

In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattice, whose continuum limit is the AKNS hierarchy. In contrast with other differential-difference versions of the AKNS…

Under the Neumann constraints, each equation of the KdV hierarchy is decomposed into two finite dimensional systems, including the well-known Neumann model. Like in the case of the Bargmann constraint, the explicit Lax representations are…

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…

Given the two boson representation of the conformal algebra \hat W_\infty, the second Hamiltonian structure of the KP hierarchy, I construct a bi-Hamiltonian hierarchy for the two associated currents. The KP hierarchy appears as a composite…

We analyze the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization (one linear factor) after 2 steps of…

Holonomy R-matrices parametrized by finite-dimensional representations are constructed for quantized universal enveloping algebras of simple Lie algebras at roots of 1.

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were…