Abstract
A general theorem on the GBDT version of the Bäcklund-Darboux transformation for systems rationally depending 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 -wave equation are reviewed. New results on explicit construction of the wave functions for radial Dirac equation are obtained.
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