### ASA 124th Meeting New Orleans 1992 October

## 3aUW1. Evolution of local spectra in smoothly varying nonhomogeneous
environments---Local canonization and marching algorithms.

**Ben Zion Steinberg
**

**
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*Dept. of Interdisciplinary Studies, Faculty of Eng., Tel-Aviv Univ.,
Tel-Aviv 69978, Israel
*

*
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A new wave equation that governs the evolution of local spectra of wave
fields in a general nonhomogeneous environment is developed. The equation is
obtained by applying the windowed Fourier transform directly to the Helmholtz
wave equation. It is shown how simple analytical solutions of the new wave
equation in a general smoothly varying nonhomogeneous environment can be
obtained using well-known analytical techniques, and how the marching
methodology connects these new solutions to the original problem described by
the Helmholtz equation.