相关论文: Darboux transformation for two-level systems
In this paper we implement the Darboux transformation, as well as an analogue of Crum's theorem, for a discrete version of Schr\"odinger equation. The technique is based on the use of first order operators intertwining two difference…
The Darboux transformation operator technique in differential and integral forms is applied to the generalized Schrodinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining…
A new approach for obtaining the transformations of solutions of nonlinear ordinary differential equations representable as the compatibility condition of the overdetermined linear systems is proposed. The corresponding transformations of…
We apply the Darboux transformation to construct new exactly-solvable cases of the two-dimensional massless Dirac equation for potential classes of Lambert-W and inverse exponential type. Both of these classes originate from the Heun…
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…
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 construct new quasi-exactly solvable one-dimensional potentials through Darboux transformations. Three directions are investigated: Reducible and two types of irreducible second-order transformations. The irreducible transformations of…
Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprisingly long time, Darboux's results were rediscovered and…
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).
We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on…
The Darboux transformation operator technique is applied to construct exactly solvable anharmonic singular oscillator potentials and to study their coherent states. Classical system corresponding to a transformed quantum system is…
As an extension of the intertwining operator idea, an algebraic method which provides a link between supersymmetric quantum mechanics and quantum (super)integrability is introduced. By realization of the method in two dimensions, two…
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mentioned, while working in the Darboux type methods, the most…
A new form of a binary Darboux transformation is used to generate analytical solutions of a nonlinear Liouville-von Neumann equation. General theory is illustrated by explicit examples.
Darboux transformations for linear operators on regular two dimensional lattices are reviewed. The six point scheme is considered as the master linear problem, whose various specifications, reductions, and their sublattice combinations lead…
For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding…
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…
With this paper we begin an investigation of difference schemes that possess Darboux transformations and can be regarded as natural discretizations of elliptic partial differential equations. We construct, in particular, the Darboux…
We present an approach to higher dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the…
The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary…