Structure of Binary Transformations of Darboux Type and Their Application to Soliton Theory
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.
English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 12, pp 2041-2059.
Citation Example: Prykarpatsky Ya. A., Samoilenko A. M., Samoilenko V. G. Structure of Binary Transformations of Darboux Type and Their Application to Soliton Theory // Ukr. Mat. Zh. - 2003. - 55, № 12. - pp. 1704-1719.