Structure of Binary Darboux-Type Transformations for Hermitian Adjoint Differential Operators - Prykarpatsky, A. K.; Samoilenko, V. G. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
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.