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Nonlinear dynamics of quadratically cubic systems
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
2013 (English)In: Physics Uspekhi, ISSN 1063-7869, E-ISSN 1468-4780, Vol. 56, no 7, 683-690 p.Article, review/survey (Refereed) Published
Abstract [en]

We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg-de Vries, and nonlinear Schrodinger partial differential equations. Some problems are solved exactly in the space-time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed.

Place, publisher, year, edition, pages
TURPION LTD, IOP PUBLISHING , 2013. Vol. 56, no 7, 683-690 p.
Keyword [en]
Equation, Waves, Media
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-6853DOI: 10.3367/UFNr.0183.201307b.0719ISI: 000325716100002Local ID: oai:bth.se:forskinfo80F85A62BECBD83EC1257C2E002E88B4OAI: oai:DiVA.org:bth-6853DiVA: diva2:834404
Available from: 2013-11-25 Created: 2013-11-25 Last updated: 2015-09-25Bibliographically approved

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Rudenko, Oleg
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