On the GBDT version of the Bäcklund-Darboux transformation and its applications to linear and nonlinear equations and Weyl theory

Abstract

A general theorem on the GBDT version of the Bäcklund-Darboux transformation for systems depending rationally on the spectral parameter is treated and its applications to nonlinear equations are given. Explicit solutions of direct and inverse problems for Dirac-type systems, including systems with singularities, and for the system auxiliary to the N-wave equation are reviewed. New results on explicit construction of the wave functions for radial Dirac equation are obtained. © EDP Sciences, 2010.