학술논문
Phase-space asymptotic analysis of wave propagation in homogeneous dispersive and dissipative media
Document Type
Periodical
Author
Source
IEEE Transactions on Antennas and Propagation IEEE Trans. Antennas Propagat. Antennas and Propagation, IEEE Transactions on. 33(11):1237-1248 Nov, 1985
Subject
Language
ISSN
0018-926X
1558-2221
1558-2221
Abstract
Arising naturally in the study of one-dimensional pulse propagation in homogeneous dispersive and/or dissipative media are certain classes of oscillatory and/or diffusion integrals which encompass the canonical diffraction catastrophe integrals due originally to Thorn and Arnold. This is especially evident within the framework of a phase-space asymptotic analysis. Depending on the order of approximation of the exact solution beyond the Liouville or "first-order quasiparticle" limit, one recognizes caustic-like structures smoothed over by hyperdiffusion. Asymptotic series for these structures, which essentially define new basic functions, have been derived, but will not be presented here. Only the salient features of these structures will be reviewed briefly, and they will be illustrated by means of several simple canonical problems. Also, their applicability to other physical areas (e.g., wave propagation in deterministically and/or randomly varying channels, diffraction, etc.) will be pointed out.