Phase-Space Approach to Wave Propagation with Dispersion and Damping

摘要

We consider dispersive propagation with damping in phase-space, and derive the Wigner distribution in terms of the initial wave and the dispersion relation. The case for no damping, that is, lossless propagation, has been previously considered by Cohen, and is a special case of the more general result presented here. Simple and physically revealing approximations of the Wigner distribution in terms of the initial Wigner distribution are presented. Also, exact low-order conditional moments are given and their interpretation is discussed.