Year: 2025
Type: article
Abstract: A technique for constructing exact solutions of nonlinear mathematical physics equations is proposed, based on the reversion of a partial sum of a perturbation method series. The latter is represented as a power series in powers of an exponential function, which is a solution of the linearized equation. The rational generating function of a sequence of coefficients of the power series is an exact solution of the original equation. The method is based on the property that the reverted power series for soliton-like solutions terminate, starting from a degree at least one greater than the order of the solution’s pole. The effectiveness of the method is demonstrated by constructing exact localized solutions of a non-integrable Korteweg-de Vries-Burgers equation, as well as nonlinear integrable differential-difference equations.
Authors: Aleksandr Zemlyanukhin, Nikolay Artamonov, Andrej Bochkarev, Vladimir Bezlyudny
Institution: Yuri Gagarin State Technical University of Saratov
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411445562