Theory of Multidimensional Delsarte–Lions Transmutation Operators. II

Document Type

Article

Publication Date

11-1-2019

Abstract

The differential-geometric and topological structures related to the Delsarte transmutation operators and the Gelfand–Levitan–Marchenko equations that describe these operators are studied by using suitable differential de Rham–Hodge–Skrypnik complexes. The correspondence between the spectral theory and special Berezansky-type congruence properties of the Delsarte transmutation operators is established. Some applications to multidimensional differential operators are presented, including the three-dimensional Laplace operator, the two-dimensional classical Dirac operator, and its multidimensional affine extension associated with self-dual Yang–Mills equations. The soliton solutions are discussed for a certain class of dynamical systems.

Identifier

85075912425 (Scopus)

Publication Title

Ukrainian Mathematical Journal

External Full Text Location

https://doi.org/10.1007/s11253-019-01689-6

e-ISSN

15739376

ISSN

00415995

First Page

921

Last Page

955

Issue

6

Volume

71

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