Structure of Binary Transformations of Darboux Type and Their Application to Soliton Theory - Prykarpatsky, Ya. A.; Samoilenko, A. M.; Samoilenko, V. G. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
On the basis of generalized Lagrange identity for pairs of formally adjoint multidimensional differential operators and a special differential geometric structure associated with this identity, we propose a general scheme of the construction of corresponding transformation operators that are described by nontrivial topological characteristics. We construct explicitly the corresponding integro-differential symbols of transformation operators, which are used in the construction of Lax-integrable nonlinear two-dimensional evolutionary equations and their Darboux–Bäcklund-type transformations.