Essentially, the Darboux proposition is based on the covariance properties of ordinary and partial differential equations with respect to a gauge transformation in the special case of second order differential equations of the SturmLiouville type. In this work, the one-dimensional Schrödinger equation with a position-dependent mass (SEPDM) is transformed into a Schrödinger-like equation with a ...

The standard binary Darboux transformation is composed and used to obtain exact multisoliton solutions of the chiral field model in two dimensions. are expressed terms quasideterminants. It has been shown that equivalent elementary transformation.

An N=(2|2) superfield formulation of the N=(2|2) supersymmetric Toda lattice hierarchy is proposed, and its five real forms are presented. 1. Introduction. Recently the N=(1|1) supersymmetric generalization of the Darboux transformation was proposed in [1], and an infinite class of bosonic and fermionic solutions of its symmetry equation was constructed in [1, 2]. These solutions generate boson...

We construct so-called Darboux matrices and fundamental solutions in the important case of generalised Hamiltonian (or canonical) systems depending rationally on spectral parameter. A wide class explicit is obtained this way. Interesting results for dynamical several variables their follow. For these purposes we use our version Bäcklund-Darboux transformation square roots corresponding matrix e...

Links of factorization theory, supersymmetry and Darboux transformations as isospectral deformations of difference operators are considered in the context of soliton theory. The dressing chain equations for factorizing operators of a spectral problem are derived. The chain equations itselves yield nonlinear systems which closure generates solutions of the equations as well as of the nonlinear s...

Abstract: We analyze a certain class of integral equations related to Marchenko equations and Gel’fand-Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution. We show how this result provides a unified approach to Darboux transformations associa...

Abstract. We present a version of q-deformed calculus based on deformed counterparts of Darboux intertwining operators. The case in which the deformed transformation function is of the vacuum type is detailed, but the extension to counterparts of excited states used as Darboux transformation functions is also formally discussed. The method leads to second-order Fokker-Planck-like deformed opera...

The nonlocal Darboux transformation for the stationary axially symmetric Schr\"odinger and Helmholtz equations is considered. Formulae are obtained its relation to generalized Moutard established. New examples of two - dimensional potencials exact solutions as an application transformation.

Two integrable lattice hierarchies associated with two discrete matrix spectral problems are derived, and the infinitely many conservation laws of the first integrable model is obtained. Moreover, the Darboux transformations based on different Darboux matrixes (2.3.4) and (3.2.4) for the above-mentioned integrable hierarchies are established with the help of two different gauge transformations ...