Related papers: On the discretization of Darboux Integrable System…
We discuss an integrable discretization of the principal chiral field models equations and its involutive reduction. We present a Darboux transformation and general construction of solution solutions for these discrete equations.
Mechanical systems are most often described by a set of continuous-time, nonlinear, second-order differential equations (SODEs) of a particular structure governed by the covariant derivative. The digital implementation of controllers for…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple…
We present the Darboux transformations for a novel class of two-dimensional discrete integrable systems named as $\mathbb{Z}_\mathcal{N}$ graded discrete integrable systems, which were firstly proposed by Fordy and Xenitidis within the…
In [5] the authors suggested a new algorithm for the numerical approximation of a BSDE by merging the cubature method with the first order discretization developed by [3] and [16]. Though the algorithm presented in [5] compared…
A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the…
We develop the Darboux procedure for the case of the two-level system. In particular, it is demonstrated that one can construct the Darboux intertwining operator that does not violate the specific structure of the equations of the two-level…
We present a series of Darboux integrable discrete equations on the square lattice. Equations of the series are numbered with natural numbers $M$. All the equations have a first integral of the first order in one of directions of the…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…
Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential…
An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…
The standard binary Darboux transformation is investigated and is used to obtain quasi-Grammian multisoliton solutions of the generalized coupled dispersionless integrable system.
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…
A $2n$-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux…
One way of constructing explicit expressions of solutions of integrable systems of Partial Differential Equations (PDEs) goes via the Darboux method. This requires the construction of Darboux matrices. Here we introduce a novel algorithm to…
In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Darboux polynomials and relies on the use of symbolic algebra…
Differential-difference equation $\frac{d}{dx}t(n+1,x)=f(x,t(n,x),t(n+1,x),\frac{d}{dx}t(n,x))$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$ is studied. We call an equation of such kind Darboux…
We introduce (binary) Darboux transformation for general differential equation of the second order in two independent variables. We present a discrete version of the transformation for a 6-point difference scheme. The scheme is appropriate…
We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted…