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On the GBDT Version of the Bäcklund-Darboux Transformation and its Applications to Linear and Nonlinear Equations and Weyl Theory

Published online by Cambridge University Press:  12 May 2010

A. Sakhnovich
A. Sakhnovich*
Affiliation:
Department of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austria
*
*E-mail: al_sakhnov@yahoo.com
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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.

Keywords

Bäcklund-Darboux transformationWeyl functionreflection coefficientdirect probleminverse problemDirac-type systemradial Dirac equationintegrable equation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 340 - 389
Copyright
© EDP Sciences, 2010

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Footnotes

To the memory of M.Sh. Birman, with deep respect

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