Central European Journal of Mathematics

, Volume 3, Issue 3, pp 529–557 | Cite as

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

  • Anatoliy Mykhaylovich Samoilenko
  • Yarema Anatoliyovych Prykarpatsky
  • Anatoliy Karolevych Prykarpatsky
Article

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 

MSC (2000)

34A30 34B05 34B15 

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Copyright information

© Central European Science Journals 2005

Authors and Affiliations

  • Anatoliy Mykhaylovich Samoilenko
    • 1
    • 2
  • Yarema Anatoliyovych Prykarpatsky
    • 1
    • 2
  • Anatoliy Karolevych Prykarpatsky
    • 2
  1. 1.The Institute of MathematicsNational Academy of SciencesKiev 01601Ukraine
  2. 2.Department of Applied MathematicsThe AGH University of Science and TechnologyKrakowPoland

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