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

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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.

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  1. Lviv University, Lviv

    Yu. M. Sydorenko

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Sydorenko, Y.M. Binary Transformations and (2 + 1)-Dimensional Integrable Systems. Ukrainian Mathematical Journal 54, 1859–1884 (2002). https://doi.org/10.1023/A:1024048625927

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