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

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...

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Bibliographic Details
Published in:Journal of physics. Conference series 2017-02, Vol.811 (1), p.12006
Main Authors: Mortell, Michael P, Seymour, Brian R
Format: Article
Language:English
Subjects:
Concentric spheres
Difference equations
Physics
Resonance
Standing waves
Travel time
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Summary: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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/811/1/012006