Exact equations for smoothed Wigner transforms and homogenization of wave propagation

Details Exact equations for smoothed Wigner transforms and homogenization of wave propagation Exact equations for smoothed Wigner transforms and homogenization of wave propagation

2006-11-19

arxiv.org/abs/math/0611564v3

Applied and Computational Harmonic Analysis, 24 (2008) pp. 378-392

Mathematics

Analysis of PDEs

16 pages, 8 figures

Scientific paper

The Wigner Transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features counterintuitive 'interference terms', which often make computation impractical. In this connection, we propose the use of the smoothed Wigner Transform (SWT), and derive new, exact equations for it, covering a broad class of wave propagation problems. Equations for spectrograms are included as a special case. The 'taming' of the interference terms by the SWT is illustrated, and an asymptotic model for the Schroedinger equation is constructed and numerically verified.

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