Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10736164 | Reports on Mathematical Physics | 2005 | 20 Pages |
Abstract
We study differential-geometric and topological structures related with Delsarte transmutations of multi-dimensional differential operators in Hilbert spaces. Based on the naturally defined de Rham-Hodge-Skrypnik differential complex the relationships with spectral theory and special Berezansky type congruence properties of Delsarte transmuted operators are stated. Some applications to multi-dimensional differential operators are done including three-dimensional Laplace operator, two-dimensional classical Dirac operator and its multidimensional affine extension, related with self-dual Yang-Mills equations. The soliton-like solutions to the related set of nonlinear dynamical systems are discussed.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Yarema A. Prykarpatsky, Anatoliy M. Samoilenko, Anatoliy K. Prykarpatsky,