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Strong and weak nonlinear dynamics: Models, classification, examples
Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
2013 (English)In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 59, no 6, 664-650 p.Article in journal (Refereed) Published
Abstract [en]

The difference between strong and weak nonlinear systems is discussed. A classification of strong nonlinearities is given. It is based on the divergence or inanity of series expansions of the equation of state commonly used in the study of weak nonlinear phenomena. Such power or functional series cannot be used in three cases: (i) if the equation of state contains a singularity; (ii) if the series diverges for strong disturbances; (iii) if the linear term is absent, and higher nonlinearity dominates. Strong nonlinearities are known in acoustics, optics, mechanics and in quantum field theory. Mathematical models, solutions and observed phenomena are presented. For example, an equation of Heisenberg type and its generalization for strongly nonlinear wave system are given. In particular, exact solutions of new “quadratically cubic” Burgers and Riemann–Hopf equations are discovered.

Place, publisher, year, edition, pages
Pleiades Publishing, Ltd. , 2013. Vol. 59, no 6, 664-650 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:bth-6628DOI: 10.1134/S1063771013060171ISI: 000326689700005Local ID: oai:bth.se:forskinfo97EAB716D75A78E8C1257C3E004EF826OAI: oai:DiVA.org:bth-6628DiVA: diva2:834151
Available from: 2014-09-04 Created: 2013-12-11 Last updated: 2017-03-16Bibliographically approved

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Rudenko, OlegHedberg, Claes
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