Binary Transformations and (2 + 1)-Dimensional Integrable Systems
A class of nonlinear nonlocal mappings that generalize the classical Darboux transformation is constructed in explicit form. Using as an example the well-known Davey–Stewartson (DS) nonlinear models and the Kadomtsev–Petviashvili matrix equation (MKP), we demonstrate the efficiency of the application of these mappings in the (2 + 1)-dimensional theory of solitons. We obtain explicit solutions of nonlinear evolution equations in the form of a nonlinear superposition of linear waves.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 11, pp 1859-1884.
Citation Example: Sidorenko Yu. M. Binary Transformations and (2 + 1)-Dimensional Integrable Systems // Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1531-1550.