Ukrainian Mathematical Journal

, Volume 55, Issue 12, pp 2041–2059 | Cite as

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

  • Ya. A. Prykarpats'kyi
  • A. M. Samoilenko
  • V. H. Samoilenko


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.


Evolutionary Equation Differential Operator General Scheme Geometric Structure Topological Characteristic 


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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Ya. A. Prykarpats'kyi
    • 1
  • A. M. Samoilenko
    • 2
  • V. H. Samoilenko
    • 3
  1. 1.Institute of Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv;University of Mining and MetallurgyKraków
  2. 2.Institute of MathematicsUkrainian Academy of SciencesKiev
  3. 3.Shevchenko Kiev UniversityKiev

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