Structure of Binary Darboux-Type Transformations for Hermitian Adjoint Differential Operators
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.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 2, pp 336-341.
Citation Example: Prikarpatskii A. K., Samoilenko V. G. Structure of Binary Darboux-Type Transformations for Hermitian Adjoint Differential Operators // Ukr. Mat. Zh. - 2004. - 56, № 2. - pp. 271-275.