title: |
The Structure of Gelfand-Levitan-Marchenko Type Equations for Delsarte Transmutation Operators of Linear Multi-Dimensional Differential Operators and Operator Pencils. Part 2 |
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publication: |
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| volume-issue: | 12 - 3 | |
| pages: | 381 - 408 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2005.12.3.5 (how to use a DOI) | |
author(s): |
Jolanta GOLENIA, Anatolij K PRYKARPATSKY, Yarema A PRYKARPATSKY |
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publication date: |
August 2005 |
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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. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |