### ASA 124th Meeting New Orleans 1992 October

## 1pUW9. Does ray chaos in range-dependent environments disappear when
higher-order approximations are made?

**Martin A. Mazur
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*Appl. Res. Lab., P.O. Box 30, State College, PA 16804
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Recent work has shown that when range dependence, in either the index of
refraction or the boundary conditions, is introduced into the infinite
frequency (ray) approximation to the wave equation, ray chaos results. This is
because the resulting conservative system of ordinary differential equations is
nonlinear and nonintegrable. Attempts have been made to reconcile chaotic ray
behavior with the fact that chaotic solutions of the full linear wave equation
cannot exist. When the terms neglected in making the eikonal approximation are
kept, the resulting system of equations is generally no longer conservative,
and hence chaos is not a necessary result of the higher-order approximation.
[Work supported by ONR.]