Group analysis of evolutionary integro-differential equations describing nonlinear waves: General model

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Full text:
Author(s): Nail H. Ibragimov, Sergey Meleshko, Oleg Rudenko
Title: Group analysis of evolutionary integro-differential equations describing nonlinear waves: General model
Journal: Journal of Physics A: Mathematical and Theoretical
Year: 2011
Volume: 44
Issue: 31
Pagination: 21
ISSN: 1751-8113
Publisher: IOP publishing
URI/DOI: 10.1088/1751-8113/44/31/315201
ISI number: 000292736300006
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
http://www.bth.se/ing/
Authors e-mail: nib@bth.se
Language: English
Abstract: The paper deals with an evolutionary integro-differential equation describing nonlinear waves. Particular choice of the kernel in the integral leads to well-known equations such as the Khokhlov-Zabolotskaya equation, the Kadomtsev-Petviashvili equation and others. Since solutions of these equations describe many physical phenomena, analysis of the general model studied in the paper equation is important. One of the methods for obtaining solutions differential equations is provided by the Lie group analysis. However, this method is not applicable to integro-differential equations. Therefore we discuss new approaches developed in modern group analysis and apply them to the general model considered in the present paper. Reduced equations and exact solutions are also presented.
Subject: Mathematics\Analysis
Mathematics\General
Mechanical Engineering\General
Keywords: Nonlinear wave, wave beam, diffraction, dispersion, relaxation, scattering, exact solutions, Lie groups, symmetries, integro-differential equation
Note: Online: stacks.iop.org/JPhysA/44/315201
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