Related papers: Miura type transformations for integrable lattices…
The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be…
A multi-component semi-discrete nonlinear integrable system associated with the relevant third-order auxiliary linear problem is claimed to be the prototype system for several reduced integrable systems formulated in terms of true dynamical…
The application of the Darboux Transformation method to the integrable model of Cylindrically Symmetrical Chiral field has been considered. The associated linear system of matrix equations has been proposed and the properties of symmetrie…
For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}. The Darboux transformation and the related…
In the present paper we consider a discretization of hyperbolic systems of exponential type. We proved that, in the case of $2\times 2$ systems, the resulting semi-discrete system is Darboux integrable only if it corresponds to a Cartan…
We give a new mechanism for constructing Backlund transformations by using symmetry reduction of differential systems. We then characterize a family of Backlund transformations between Darboux integrable systems where the Backlund…
Several integrable semi-discretizations are known in the literature for the massive Thirring system in characteristic coordinates. We present for the first time an integrable semi-discretization of the massive Thirring system in laboratory…
Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete…
Darboux transformations are employed in construction and analysis of Dirac Hamiltonians with pseudoscalar potentials. By this method, we build a four parameter class of reflectionless systems. Their potentials correspond to composition of…
Darboux transformation plays a key role in constructing explicit closed-form solutions of completely integrable systems. This paper provides an algebraic construction of generalized Darboux matrices with the same poles for the $2\times2$…
A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main…
We present a systematic approach to the construction of Miura transformations for discrete Painlev\'e equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of…
We have undertaken an algorithmic search for new integrable semi-discretizations of physically relevant nonlinear partial differential equations. The search is performed by using a compatibility condition for the discrete Lax operators and…
Using a general result of bidifferential calculus and recent results of other authors, a vectorial binary Darboux transformation is derived for the first member of the "negative" part of the potential Kaup-Newell hierarchy, which is a…
We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the…
We present a nonlinear partial difference equation defined on a square which is obtained by combining the Miura transformations between the Volterra and the modified Volterra differential-difference equations. This equation is not symmetric…
In this paper the Mikhailov model is discretized by means of the Cauchy matrix approach. A pair of discrete Miura transformations are constructed. The discrete Mikhailov model is a coupled system, in which one equation comes from the…
We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2+1 dimensions, such as the dispersionless Kadomtsev-Petviashvili (dKP) and dispersionless Toda lattice (dTl) equations, can be deformed into reductions of…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. A new coupled system related to the recently found lattice is presented. A method for eliminating…
Several types of Darboux transformations for supersymmetric integrable systems such as the Manin-Radul KdV, Mathieu KdV and SUSY sine-Gordon equations are considered. We also present solutions such as supersolitons and superkinks.