Math. Model. Nat. Phenom.
Volume 14, Number 4, 2019
Singular perturbations and multiscale systems
|Number of page(s)||20|
|Published online||05 April 2019|
The evolution of resonance: a multiscale approach to the effect of nonlinearity, frequency dispersion and geometry
Department of Applied Mathematics, University College Cork,
2 Department of Mathematics, University of British Columbia, Vancouver, Canada.
* Corresponding author: email@example.com
Accepted: 30 January 2019
Nonlinear resonant oscillations in continuous media contain two natural time scales: the travel time in the medium and the ‘slow’ time defined by the small nonlinearity. A multiscale approach is used to describe the evolution to a periodic state. We focus on three basic experiments that define nonlinear resonant oscillations in continuous media: a gas in both a straight tube and a tube of variable cross-section, and shallow water in a tank. The outcomes of these experiments are described and the mathematical techniques that show the evolution to the final periodic states are given in some detail.
Mathematics Subject Classification: 35L05 / 35L67
Key words: Nonlinear wave / resonance / evolution
© EDP Sciences, 2019
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