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Structure of Binary Darboux-Type Transformations for Hermitian Adjoint Differential Operators
Authors:A K Prykarpats'kyi  V H Samoilenko
Institution:(1) AGH University of Science and Technology, Kraków, Poland;;(2) Institute for Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv;(3) Shevchenko Kiev University, Kiev
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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