2017
Том 69
№ 9

All Issues

Binary Transformations and (2 + 1)-Dimensional Integrable Systems

Sidorenko Yu. M.

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Abstract

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.

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