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/).
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 -