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 |
