Nonlinearization and waves in bounded media: old wine in a new bottle

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Date
2017-03
Authors
Mortell, Michael P.
Seymour, Brian R.
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IOP Publishing
Published Version
10.1088/1742-6596/811/1/012006
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Abstract
We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.
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Keywords
Wave reflections , Oscillation , Resonance , Hyperbolic waves
Citation
Mortell, M. P. and Seymour, B. R. (2017) 'Nonlinearization and waves in bounded media: old wine in a new bottle', Journal of Physics: Conference Series, 811(1), pp. 012006. doi:10.1088/1742-6596/811/1/012006
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https://hdl.handle.net/10468/3772
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Mathematical Sciences- Journal Articles
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© 2017. Published under licence in Journal of Physics: Conf. Series by IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the authors and the title of the work, journal citation and DOI.