1. An interesting class of real functions of a single real variable, the approximately continuous functions, was introduced by Denjoy [l] in his work on derivatives. The two principal facts discovered by Denjoy are that these functions are of Baire class 1 and have the Darboux property. Ridder [2] showed that the arguments of Denjoy apply to real functions of n variables. In this paper we discu...

The technique of Darboux transformation is applied to nonlocal partner of two– dimensional periodic An−1 Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The connect...

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 to solving a hyperbolic type initial-boundary value problem. We discuss several reductions and specifications of the transformations as well as construction ...

Using calculated phaseshift values, for pp, nn, and np elastic scattering in the energy range 1MeV to 350MeV, the charge independence breaking of nucleon-nucleon interaction is investigated. We have used Darboux transformation to calculate phase-shift for the first three values of l. It is seen that the charge independency holds in most of the energy range but it is broken in the particular ene...

Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at least a Levy transformation in each direction, we get closed formulae in terms of multiWroński determinants. These formulae are for the tangent vectors, Lamè coefficients, rotation coefficients and points of the surface...

A version of the iterated Bäcklund-Darboux transformation, where Darboux matrix takes a form of the transfer matrix function from the system theory, is constructed for the discrete canonical system and Non-Abelian Toda lattice. Results on the transformations of the Weyl functions, insertion of the eigenvalues, and construction of the bound states are obtained. A wide class of the explicit solut...

The vectorial extension of the Ribaucour transformation for the Lamé equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which it follows the permutability of the vectorial Ribaucour transformations. Finally, as an exam...

The structure properties of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces is studied by means of differential-geometric and topological tools. It is shown that kernels of the corresponding integral operator expressions depend on the topological structure of related homological cycles in the coordinate space. As a natural realization of the constructio...

The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger type which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for and then construct its quasideterminant solutions. multisoliton breather solutions are given explicitly.