相关论文: Darboux transformations for 5-point and 7-point se…

The Fokker-Planck equation associated with the two - dimensional stationary Schr\"odinger equation has the conservation low form that yields a pair of potential equations. The special form of Darboux transformation of the potential…

We show here that matrix Darboux-Toda transformation can be written as a product of a number of mappings. Each of these mappings is a symmetry of the matrix nonlinear Shrodinger system of integro-differential equations. We thus introduce a…

Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn).

In this letter, for the discrete parity-time-symmetric nonlocal nonlinear Schr\"{o}dinger equation, we construct the Darboux transformation, which provides an algebraic iterative algorithm to obtain a series of analytic solutions from a…

We construct explicit Darboux transformations for a generalized, two-dimensional Dirac equation. Our results contain former findings for the one-dimensional, stationary Dirac equation, as well as for the fully time-dependent case in (1+1)…

We show how to derive noncommutative versions of integrable partial difference equations using Darboux transformations. As an illustrative example, we use the nonlinear Schr\"odinger (NLS) system. We derive a noncommutative nonlinear…

We study the discretization of Darboux integrable systems. The discretization is done using $x$-, $y$-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.

A nonlocal derivative nonlinear Schrodinger equation is introduced. By constructing its basic Darboux transformations of degrees one and two, the explicit expressions of new solutions are derived from seed solutions by Darboux…

In this paper we derive new two-component integrable differential difference and partial difference systems by applying a Lax-Darboux scheme to an operator formed from an ${\mathfrak{sl}}_3({\mathbb{C}})$-based automorphic Lie algebra. The…

A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined…

The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac…

We introduce the sub-lattice approach, a procedure to generate, from a given integrable lattice, a sub-lattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point…

A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…

The nonlocal Darboux transformation of the stationary axially symmetric Schr\"odinger equation is considered. It is shown that a special case of the nonlocal Darboux transformation provides the generalization of the Moutard transformation.…

The nonlocal Darboux transformation for the stationary axially symmetric Schr\"odinger and Helmholtz equations is considered. Formulae for the nonlocal Darboux transformation are obtained and its relation to the generalized Moutard…

In this thesis we study the Darboux transformations related to particular Lax operators of NLS type which are invariant under the action of the so-called reduction group. Specifically, we study the cases of: 1) the nonlinear Schr\"odinger…

Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes…

The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and the method of additional independent variables. Then the…

An "exact discretization" of the Schroedinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can…

An integrable self-adjoint 7-point scheme on the triangular lattice and an integrable self-adjoint scheme on the honeycomb lattice are studied using the sublattice approach. The star-triangle relation between these systems is introduced,…