Structure of Binary Darboux-Type Transformations for Hermitian Adjoint Differential Operators |
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Authors: | A K Prykarpats'kyi V H Samoilenko |
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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 |
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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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