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The quadratically cubic Burgers equation: an exactly solvable nonlinear model for shocks, pulses and periodic waves
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
2016 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 85, no 2, 767-776 p.Article in journal (Refereed) Published
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Abstract [en]

A modified equation of Burgers type with a quadratically cubic (QC) nonlinear term was recently pointed out as a new exactly solvable model of mathematical physics. However, its derivation, analytical solution, computer modeling, as well as its physical applications and analysis of corresponding nonlinear wave phenomena have not been published up to now. The physical meaning and generality of this QC nonlinearity are illustrated here by several examples and experimental results. The QC equation can be linearized and it describes the experimentally observed phenomena. Some of its exact solutions are given. It is shown that in a QC medium not only shocks of compression can be stable, but shocks of rarefaction as well. The formation of stationary waves with finite width of shock front resulting from the competition between nonlinearity and dissipation is traced. Single-pulse propagation is studied by computer modeling. The nonlinear evolutions of N- and S-waves in a dissipative QC medium are described, and the transformation of a harmonic wave to a sawtooth-shaped wave with periodically recurring trapezoidal teeth is analyzed. © 2016 The Author(s)

Place, publisher, year, edition, pages
Springer Netherlands, 2016. Vol. 85, no 2, 767-776 p.
Keyword [en]
Acoustics; Control nonlinearities; Linearization; Mathematical transformations; Nonlinear systems; Partial differential equations; Shear waves; Shock waves, Cubic equations; Exact analytical solutions; Exact linearization; Non-linear acoustics; Nonlinear partial differential equations; Shock fronts; Strongly nonlinear system, Nonlinear equations
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Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:bth-11867DOI: 10.1007/s11071-016-2721-5ISI: 000378410800006Scopus ID: 2-s2.0-84962622283OAI: oai:DiVA.org:bth-11867DiVA: diva2:925695
Available from: 2016-05-03 Created: 2016-05-02 Last updated: 2017-06-19Bibliographically approved

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Rudenko, OlegHedberg, Claes
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CiteExportLink to record
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  • apa
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