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Nonlinearization and waves in bounded media: old wine in a new bottle
Mortell, Michael P.; Seymour, Brian R.
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.
Keyword(s): Wave reflections; Oscillation; Resonance; Hyperbolic waves
Publication Date:
2017
Type: Journal article
Peer-Reviewed: Yes
Language(s): English
Institution: University College Cork
Citation(s): 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
Publisher(s): IOP Publishing
File Format(s): application/pdf
First Indexed: 2017-03-14 06:17:00 Last Updated: 2019-01-11 06:58:03