Journal of Nonlinear Mathematical Physics

Volume 12, Issue 3, August 2005, Pages 381 - 408

The Structure of Gelfand-Levitan-Marchenko Type Equations for Delsarte Transmutation Operators of Linear Multi-Dimensional Differential Operators and Operator Pencils. Part 2

Authors
Jolanta Golenia, Anatolij K. Prykarpatsky, Yarema A. Prykarpatsky
Corresponding Author
Jolanta Golenia
Received 23 June 2004, Accepted 22 October 2004, Available Online 1 August 2005.
DOI
10.2991/jnmp.2005.12.3.5How to use a DOI?
Abstract

The differential-geometric and topological structure of Delsarte transmutation opertors their associated Gelfand-Levitan-Marchenko type equations are studied making use of the de Rham-Hodge-Skrypnik differential complex. The relationships with spetral theory and special Berezansky type congruence properties of Delsarte transmuted operators are stated. Some applications to multi-dimensional differential operators are done including the three-dimensional Laplace operator and the two-dimensional classical Dirac operator and its multi-dimensional affine extension, related with seldual Yang-Mills equations. The soliton like solutions to the related set of nonlinear dynamical systems are discussed.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - 3
Pages
381 - 408
Publication Date
2005/08/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2005.12.3.5How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Jolanta Golenia
AU  - Anatolij K. Prykarpatsky
AU  - Yarema A. Prykarpatsky
PY  - 2005
DA  - 2005/08/01
TI  - The Structure of Gelfand-Levitan-Marchenko Type Equations for Delsarte Transmutation Operators of Linear Multi-Dimensional Differential Operators and Operator Pencils. Part 2
JO  - Journal of Nonlinear Mathematical Physics
SP  - 381
EP  - 408
VL  - 12
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.3.5
DO  - 10.2991/jnmp.2005.12.3.5
ID  - Golenia2005
ER  -