| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
|
|
|---|---|---|
| Page(s) | 340 - 389 | |
| DOI | https://doi.org/10.1051/mmnp/20105415 | |
| Published online | 12 May 2010 | |
On the GBDT Version of the Bäcklund-Darboux Transformation and its Applications to Linear and Nonlinear Equations and Weyl Theory
Department of Mathematics, University of Vienna,
Nordbergstrasse 15,
A-1090
Vienna, Austria
* E-mail: al_sakhnov@yahoo.com
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.
Mathematics Subject Classification: 37K35 / 34B20 / 47A48 / 37K10 / 47A40
Key words: Bäcklund-Darboux transformation / Weyl function / reflection coefficient / direct problem / inverse problem / Dirac-type system / radial Dirac equation / integrable equation
© EDP Sciences, 2010
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