Weak chaos in an area-preserving mapping for sound ray propagation

A nonseparable underwater acoustic wave propagation problem is studied in the geometric limit. The combination of internal refraction and reflecting boundaries leads to a noncontinuously differentiable area-preserving mapping, to which the KAM theorem does not apply. The phenomenon of weak chaos, wh...

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Bibliographic Details
Published in:Physics letters. A 1991-03, Vol.153 (4), p.181-185
Main Authors: Tappert, Frederick D., Brown, Michael G., Goñi, Gustavo
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Physics
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Summary:A nonseparable underwater acoustic wave propagation problem is studied in the geometric limit. The combination of internal refraction and reflecting boundaries leads to a noncontinuously differentiable area-preserving mapping, to which the KAM theorem does not apply. The phenomenon of weak chaos, wherein an arbitrarily small perturbation to the separable problem causes observable chaotic behavior, is shown to occur.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(91)90790-F