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Group analysis of evolutionary integro-differential equations describing nonlinear waves: General model
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2011 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 44, no 31Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
IOP publishing , 2011. Vol. 44, no 31
Keyword [en]
Nonlinear wave, wave beam, diffraction, dispersion, relaxation, scattering, exact solutions, Lie groups, symmetries, integro-differential equation
National Category
Mathematics Mathematical Analysis Applied Mechanics
URN: urn:nbn:se:bth-7214DOI: 10.1088/1751-8113/44/31/315201ISI: 000292736300006Local ID: diva2:834796
Online: from: 2012-11-12 Created: 2011-07-06 Last updated: 2015-06-30Bibliographically approved

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Rudenko, Oleg
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