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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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