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

Abstract

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.