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...

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 ...

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...

New family of flat potential (Darboux-Egoroff) metrics on the Hurwitz spaces and corresponding Frobenius structures are found. We consider a Hurwitz space as a real manifold. Therefore the number of coordinates is twice as big as the number of coordinates used in the construction of Frobenius manifolds on Hurwitz spaces found by B.Dubrovin more than 10 years ago. The branch points of a ramified...

The method of constructing spectral Darboux coordinates on finite dimensional coadjoint orbits in duals of loop algebras is applied to the one pole case, where the orbit is identified with a coadjoint orbit in the dual of a finite dimensional Lie algebra. The constructions are carried out explicitly when the Lie algebra is sl(2,R), sl(3,R), and so(3,R), and for rank two orbits in so(n,R). A new...

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...

A review of the uses of the CD kernel in the spectral theory of orthogonal polynomials, concentrating on recent results.

We show how the Witten-Dijkgraff-Verlinde-Verlinde (WDVV) equations and the Darboux-Zakharov-Manakov (DZM) system can be characterized via a background family of functions.