We show that any classical matrix Q × Q S-integrable Partial Differential Equation (PDE) obtainable as commutativity condition of a certain type of vector fields possesses a family of lower-dimensional reductions represented by the matrix Q × n 0 Q quasilinear first order PDEs solved in [29] by the method of characteristics. In turn, these PDEs admit two types of available particular solutions:...

We show that matrix Q × Q Self-dual type S-integrable Partial Differential Equations (PDEs) possess a family of lower-dimensional reductions represented by the matrix Q × n 0 Q quasilinear first order PDEs solved in [29] by the method of characteristics. In turn, these PDEs admit two types of available particular solutions: (a) explicit solutions and (b) solutions described implicitly by a syst...

We consider a hierarchy of classical Liouville completely integrable models sharing the same (linear) r–matrix structure obtained through an N–th jet–extension of su(2) rational Gaudin models. The main goal of the present paper is the study of the integrable model corresponding to N = 3, since the case N = 2 has been considered by the authors in separate papers, both in the one–body case (Lagra...

We apply a 3-dimensional approach to describe a new parametrization of the L-operators for the 2-dimensional Bazhanov-Stroganov (BS) integrable spin model related to the chiral Potts model. This parametrization is based on the solution of the associated classical discrete integrable system. Using a 3-dimensional vertex satisfying a modified tetrahedron equation, we construct an operator which g...

We present a general formulation of the matrix product ansatz for exactly integrable chains on periodic lattices. This new formulation extends the matrix product ansatz present on our previous articles ( F. C. Alcaraz and M. J. Lazo J. Phys. A: Math. Gen. 37 (2004) L1-L7 and J. Phys. A: Math. Gen. 37 (2004) 4149-4182.) In [1] (to which we refer hereafter as I) and [2], we formulate a matrix pro...

We study matrix generalizations of derivative nonlinear Schrödinger-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’ in Calogero’s terminology. PACS numbers: 02.10Jf, 02.30.Jr, 03.65.Ge, 11.30.-j Submitted to: Inverse Problems † E-mail address: [email protected]...

We propose the exact boundary S matrix for breathers of theN = 2 supersymmetric sine-Gordon model. We argue that this S matrix has three independent parameters, in agreement with a recently-proposed action. We also show, contrary to a previous claim, that the “universal” supersymmetric boundary S matrix commutes with two supersymmetry charges. General N = 2 supersymmetric boundary integrable mo...

We study level statistics in ensembles of integrable N×N matrices linear in a real parameter x. The matrix H(x) is considered integrable if it has a prescribed number n>1 of linearly independent commuting partners H^{i}(x) (integrals of motion) [H(x),H^{i}(x)]=0, [H^{i}(x),H^{j}(x)]=0, for all x. In a recent work [Phys. Rev. E 93, 052114 (2016)2470-004510.1103/PhysRevE.93.052114], we developed ...

The centrally extended superalgebra psu(2|2)⋉ R 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 Uq(psu(2|2)⋉R) and derive the fundamental R-matrix. From the latter we deduce an integrable spin chain Hamiltonian with three independent parameters and the corres...

Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)dimensional case, the corresponding system can be extended to 2 × 2 matrix form. The factorization theorem of the Christoffel kernel for s...