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Structure of Binary Darboux-Type Transformations for Hermitian Adjoint Differential Operators

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Ukrainian Mathematical Journal Aims and scope

Abstract

For Hermitian adjoint differential operators, we consider the structure of Darboux–Bäcklund-type transformations in the class of parametrically dependent Hilbert spaces. By using the proposed new method, we obtain the corresponding integro-differential symbols of the operators of transformations in explicit form and consider the problem of their application to the construction of two-dimensional Lax-integrable nonlinear evolution equations and their Darboux–Bäcklund-type transformations.

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Authors and Affiliations

  1. AGH University of Science and Technology, Kraków, Poland;

    A. K. Prykarpats'kyi

  2. Institute for Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv

    A. K. Prykarpats'kyi

  3. Shevchenko Kiev University, Kiev

    V. H. Samoilenko

Authors
  1. A. K. Prykarpats'kyi
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  2. V. H. Samoilenko
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Prykarpats'kyi, A.K., Samoilenko, V.H. Structure of Binary Darboux-Type Transformations for Hermitian Adjoint Differential Operators. Ukrainian Mathematical Journal 56, 336–341 (2004). https://doi.org/10.1023/B:UKMA.0000036107.23520.fc

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  • DOI: https://doi.org/10.1023/B:UKMA.0000036107.23520.fc

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