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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo


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Volume 3, Issue 3

Issues

Volume 13 (2015)

The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension

Anatoliy Samoilenko / Yarema Prykarpatsky / Anatoliy Prykarpatsky
Published Online: 2005-09-01 | DOI: https://doi.org/10.2478/BF02475922

Abstract

The differential-geometric and topological structure of Delsarte transmutation operators and their associated Gelfand-Levitan-Marchenko type eqautions are studied along with classical Dirac type operator and its multidimensional affine extension, related with selfdual Yang-Mills eqautions. The construction of soliton-like solutions to the related set of nonlinear dynamical system is discussed.

Keywords: Delsarte transmutation operators; parametric functional spaces; Darboux transformations; inverse spectral transform problem; soliton equations; generalized de Rham-Hodge differential complex; Zakharov-Shabat equations; Laplace and Dirac type operators

Keywords: 34A30; 34B05; 34B15

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About the article

Published Online: 2005-09-01

Published in Print: 2005-09-01


Citation Information: Open Mathematics, Volume 3, Issue 3, Pages 529–557, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02475922.

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© 2005 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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