Strong and weak nonlinear dynamics: Models, classification, examples
2013 (English)In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 59, no 6, 664-650 p.Article in journal (Refereed) Published
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.
Fluid Mechanics and Acoustics
IdentifiersURN: urn:nbn:se:bth-6628DOI: 10.1134/S1063771013060171ISI: 000326689700005Local ID: oai:bth.se:forskinfo97EAB716D75A78E8C1257C3E004EF826OAI: oai:DiVA.org:bth-6628DiVA: diva2:834151