On the GBDT Version of the Bäcklund-Darboux Transformation and its Applications to Linear and Nonlinear Equations and Weyl Theory
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 4, pp. 340-389.

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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.
DOI : 10.1051/mmnp/20105415

A. Sakhnovich 1

1 Department of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austria
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A. Sakhnovich. On the GBDT Version of the Bäcklund-Darboux Transformation and its Applications to Linear and Nonlinear Equations and Weyl Theory. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 4, pp. 340-389. doi : 10.1051/mmnp/20105415. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20105415/

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