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Structure of Binary Transformations of Darboux Type and Their Application to Soliton Theory

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Abstract

On the basis of generalized Lagrange identity for pairs of formally adjoint multidimensional differential operators and a special differential geometric structure associated with this identity, we propose a general scheme of the construction of corresponding transformation operators that are described by nontrivial topological characteristics. We construct explicitly the corresponding integro-differential symbols of transformation operators, which are used in the construction of Lax-integrable nonlinear two-dimensional evolutionary equations and their Darboux–Bäcklund-type transformations.

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Authors and Affiliations

  1. Institute of Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv;, University of Mining and Metallurgy, Kraków

    Ya. A. Prykarpats'kyi

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. M. Samoilenko

  3. Shevchenko Kiev University, Kiev

    V. H. Samoilenko

Authors
  1. Ya. A. Prykarpats'kyi
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  2. A. M. Samoilenko
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  3. V. H. Samoilenko
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Prykarpats'kyi, Y.A., Samoilenko, A.M. & Samoilenko, V.H. Structure of Binary Transformations of Darboux Type and Their Application to Soliton Theory. Ukrainian Mathematical Journal 55, 2041–2059 (2003). https://doi.org/10.1023/B:UKMA.0000031664.23436.5a

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  • DOI: https://doi.org/10.1023/B:UKMA.0000031664.23436.5a

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