Abstract
The initial-value problems for acoustic waves in fluids, elastic waves in solids and electromagnetic waves are discussed. The governing systems of first-order partial differential equations pertaining to arbitrarily inhomogenous and anisotropic media are taken as point of departure and, correspondingly, the initial values of the pertaining two state quantities (i.e. the two quantities whose product specifies the area density of power flow in each of the wave motions) are prescribed. The initial-value problem thus posed is thought to be more physical (and turns out to be more complicated) than the conventional one associated with the second-order wave equation in one of the two state quantities, where the inital values of this state quantity and its first-order time derivative are prescribed. For the cases of homogeneous, isotropic media, the initial-value problems are solved with the aid of a time Laplace and spatial Fourier transform method that bears resemblance to the modified Cagniard method for solving transient wave propagation problems in layered media.
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