New features of backlund and darboux transformations in 2 + 1 dimensions

Abstract

Backlund transformations of the time-dependent Schrodinger equation which transform a real potential into another real potential are constructed, as well as their Darboux versions. The iterated application of these Backlund transformations to a generic potential is considered and the obtained recursion relations are explicitly solved. It is shown that the dressing of the generic potential can be obtained by taking the continuous limit of this infinite sequence of Backlund transformations, and that the delta -bar integral equations, which solve the inverse spectral problem, can be obtained as the continuous limit of the recurrence equation defining the sequence of the Darboux transformations.