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SINGLE SHOCK AND PERIODIC SAWTOOTH-SHAPED WAVES IN MEDIA WITH NON-ANALYTIC NONLINEARITIES
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Blekinge Inst Technol, S-37179 Karlskrona, Sweden..ORCID iD: 0000-0001-8739-4492
2018 (English)In: Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, E-ISSN 1760-6101, Vol. 13, no 2, article id UNSP 18Article in journal (Refereed) Published
Abstract [en]

The review of new mathematical models containing non-analytic nonlinearities is given. These equations have been proposed recently, over the past few years. The models describe strongly nonlinear waves of the first type, according to the classification introduced earlier by the authors. These models are interesting because of two reasons: (i) equations admit exact analytic solutions, and (ii) solutions describe the real physical phenomena. Among these models are modular and quadratically cubic equations of Hopf, Burgers, Korteveg-de Vries, Khokhlov-Zabolotskaya and Ostrovsky-Vakhnenko type. Media with non-analytic nonlinearities exist among composites, meta-materials, inhomogeneous and multiphase systems. Some physical phenomena manifested in the propagation of waves in such media are described on the qualitative level of severity.

Place, publisher, year, edition, pages
EDP SCIENCES S A , 2018. Vol. 13, no 2, article id UNSP 18
Keywords [en]
Equations of Hopf, Burgers, KdV, KZ and Ostrovsky-Vakhnenko types, exact solutions, modular solutions, quadratically-cubic nonlinearity, shocks of rarefaction, triangular and trapezoidal saw
National Category
Other Mathematics Other Mechanical Engineering
Identifiers
URN: urn:nbn:se:bth-17017DOI: 10.1051/mmnp/2018028ISI: 000443894600003OAI: oai:DiVA.org:bth-17017DiVA, id: diva2:1249677
Available from: 2018-09-20 Created: 2018-09-20 Last updated: 2018-09-20Bibliographically approved

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Rudenko, OlegHedberg, Claes

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