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

A. Sakhnovich

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 4, page 340-389
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Sakhnovich, A.. "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 5.4 (2010): 340-389. <http://eudml.org/doc/197668>.

@article{Sakhnovich2010,
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.},
author = {Sakhnovich, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {Bäcklund-Darboux transformation; Weyl function; reflection coefficient; direct problem; inverse problem; Dirac-type system; radial Dirac equation; integrable equation},
language = {eng},
month = {5},
number = {4},
pages = {340-389},
publisher = {EDP Sciences},
title = {On the GBDT Version of the Bäcklund-Darboux Transformation and its Applications to Linear and Nonlinear Equations and Weyl Theory},
url = {http://eudml.org/doc/197668},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Sakhnovich, A.
TI - On the GBDT Version of the Bäcklund-Darboux Transformation and its Applications to Linear and Nonlinear Equations and Weyl Theory
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/5//
PB - EDP Sciences
VL - 5
IS - 4
SP - 340
EP - 389
AB - 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.
LA - eng
KW - Bäcklund-Darboux transformation; Weyl function; reflection coefficient; direct problem; inverse problem; Dirac-type system; radial Dirac equation; integrable equation
UR - http://eudml.org/doc/197668
ER -

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