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Equation admitting linearization and describing waves in dissipative media with modular, quadratic, and quadratically cubic nonlinearities
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
2016 (English)In: Doklady Mathematics, ISSN 1064-5624, Vol. 94, no 3, 703-707 p.Article in journal (Refereed) Published
Abstract [en]

A second-order partial differential equation admitting exact linearization is discussed. It contains terms with nonlinearities of three types—modular, quadratic, and quadratically cubic—which can be present jointly or separately. The model describes nonlinear phenomena, some of which have been studied, while others call for further consideration. As an example, individual manifestations of modular nonlinearity are discussed. They lead to the formation of singularities of two types, namely, discontinuities in a function and discontinuities in its derivative, which are eliminated by dissipative smoothing. The dynamics of shock fronts is studied. The collision of two single pulses of different polarity is described. The process reveals new properties other than those of elastic collisions of conservative solitons and inelastic collisions of dissipative shock waves.

Place, publisher, year, edition, pages
Maik Nauka/Interperiodica, 2016. Vol. 94, no 3, 703-707 p.
Keyword [en]
BURGERS-EQUATION; MODEL
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Identifiers
URN: urn:nbn:se:bth-13795DOI: 10.1134/S1064562416060053ISI: 000392142200024ScopusID: 2-s2.0-85008700671OAI: oai:DiVA.org:bth-13795DiVA: diva2:1067241
Available from: 2017-01-20 Created: 2017-01-20 Last updated: 2017-02-22Bibliographically approved

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Rudenko, Oleg
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