Transient waves in non-stationary media

In English This paper treats propagation of transient waves in non-stationary media,
which has many applications in e.g. electromagnetics and acoustics. The underlying
hyperbolic equation is a general, homogeneous, linear, first order 2×2
system of equations. The coefficients in this system depend only on one spatial
coordinate and time. Furthermore, memory effects are modeled by integral
kernels, which, in addition to the spatial dependence, are functions of two different
time coordinates. These integrals generalize the convolution integrals,
frequently used as a model for memory effects in the medium. Specifically, the
scattering problem for this system of equations is addressed. This problem is
solved by a generalization of the wave splitting concept, originally developed
for wave propagation in media which are invariant under time translations,
and by an imbedding or a Green functions technique. More explicitly, the
imbedding equation for the reflection kernel and the Green functions (propagator
kernels) equations are derived. Special attention is paid to the problem
of non-stationary characteristics. A few numerical examples illustrate this
problem.