| Issue |
Math. Model. Nat. Phenom.
Volume 14, Number 4, 2019
Singular perturbations and multiscale systems
|
|
|---|---|---|
| Article Number | 403 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/mmnp/2019005 | |
| Published online | 05 April 2019 | |
The evolution of resonance: a multiscale approach to the effect of nonlinearity, frequency dispersion and geometry
1
Department of Applied Mathematics, University College Cork,
Cork, Ireland.
2
Department of Mathematics, University of British Columbia,
Vancouver, Canada.
* Corresponding author: seymour@math.ubc.ca
Received:
25
September
2018
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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