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Self-similar solutions of a Burgers-type equation with quadratically cubic nonlinearity
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
2016 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 93, no 1, 94-98 p.Article in journal (Refereed) PublishedText
Abstract [en]

Self-similar solutions are found for a quadratically cubic second-order partial differential equation governing the behavior of nonlinear waves in various distributed systems, for example, in some metamaterials. They are compared with self-similar solutions of the Burgers equation. One of them describing a single unipolar pulse is shown to satisfy both equations. The other self-similar solutions of the quadratically cubic equation behave differently from the solutions of the Burgers equation. They are constructed by matching the positive and negative branches of the solution, so that the function itself and its first derivative are continuous. One of these solutions corresponds to an asymmetric solitary N-wave of the sonic shock type. Self-similar solutions of a quadratically cubic equation describing the propagation of cylindrically symmetric waves are also found.

Place, publisher, year, edition, pages
Maik Nauka/Interperiodica, 2016. Vol. 93, no 1, 94-98 p.
National Category
Mechanical Engineering
URN: urn:nbn:se:bth-11851DOI: 10.1134/S1064562416010051ISI: 000373359900025OAI: diva2:925536
Available from: 2016-05-02 Created: 2016-05-02 Last updated: 2016-05-03Bibliographically approved

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Rudenko, Oleg
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