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

An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries,…

We present an affine $sl (n+1)$ algebraic construction of the basic constrained KP hierarchy. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax…

For the rational, elliptic and trigonometric r-matrices, we exhibit the links between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral…

By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as…

We introduce a canonical operator-theoretic construction associated to a finite geometric lattice, in which a simple nonassociative ``diamond product'' on the lattice basis gives rise to a family of creation operators indexed by atoms and a…

A systematic way of construction of (1+1)-dimensional dispersionless integrable Hamiltonian systems is presented. The method is based on the classical R-matrix on Poisson algebras of formal Laurent series. Results are illustrated with the…

Modified $r$-matrices are solutions of the modified classical Yang-Baxter equation, introduced by Semenov-Tian-Shansky, and play important roles in mathematical physics. In this paper, first we introduce a cohomology theory for modified…

In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a…

We consider some algebraic and geometric aspects of the theory of integrable systems in finite dimensions, associated with the existence of a classical $r$-matrix, first introduced by Sklyanin as the classical analogue of the quantum…

We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda Lattice hierarchy (2DTL). This reduction implies that the RTC is gauge equivalent to the discrete AKNS hierarchy and,…

We prove that the Kupershmidt deformation of a bi-Hamiltonian system is itself bi-Hamiltonian. Moreover, Magri hierarchies of the initial system give rise to Magri hierarchies of Kupershmidt deformations as well. Since Kupershmidt…

The dispersionless KP and Toda hierarchies possess an underlying twistorial structure. A twistorial approach is partly implemented by the method of Riemann-Hilbert problem. This is however still short of clarifying geometric ingredients of…

The centrally extended superalgebra psu(2|2)xR^3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation…

The Riemann hierarchy is the simplest example of rank one, ($1$+$1$)-dimensional integrable system of nonlinear evolutionary PDEs. It corresponds to the dispersionless limit of the Korteweg-de Vries hierarchy. In the language of formal…

Following Natanzon-Zabrodin, we explore the Kadomtsev-Petviashvili hierarchy as an infinite system of mutually consistent relations on the second derivatives of the free energy with some universal coefficients. From this point of view,…

We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential…

R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the…

A fairly complete list of Toda-like integrable lattice systems, both in the continuous and discrete time, is given. For each system the Newtonian, Lagrangian and Hamiltonian formulations are presented, as well as the 2x2 Lax representation…

The aim of the paper is to build a universal R-matrix for the multiparameter deformation of any reductive Lie algebra. Such deformations, formulated in the recent past by Truini and Varadarajan, have the property of universality in a…

The Hamiltonian approach to isomonodromic deformation systems for generic rational covariant derivative operators on the Riemann sphere, having any matrix dimension $r$ and any number of isolated singularities of arbitrary Poincar\'e rank,…