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Exact solutions of an integro-differential 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. 94, no 1, 468-471 p.Article in journal (Refereed) Published
Abstract [en]

Exact solutions of a nonlinear integro-differential equation with quadratically cubic nonlinear term are found. The equation governs, in particular, stationary shock wave propagation in relaxing media. For the exponential kernel the shapes of both compression and rarefaction shocks having a finite width of the front are calculated. For media with limited "memorizing time" the difference relation permitting the construction of wave profile by the mapping method is derived. The initial equation is rather general. It governs the evolution of nonlinear waves in real distributed systems, for example, in biological tissues, structurally inhomogeneous media and in some meta-materials.

Place, publisher, year, edition, pages
Maik Nauka/Interperiodica, 2016. Vol. 94, no 1, 468-471 p.
National Category
Other Mathematics
URN: urn:nbn:se:bth-13053DOI: 10.1134/S1064562416040050ISI: 000382860900027OAI: diva2:1002468
Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2016-11-10Bibliographically approved

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Rudenko, Oleg
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