Advanced

Transient waves in nonstationary media

Åberg, Ingegerd; Kristensson, Gerhard LU and Wall, David J. N. (1996) In Journal of Mathematical Physics 37(5). p.2229-2252
Abstract
This paper treats propagation of transient waves in nonstationary media, which has many applications in, for example, 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 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... (More)
This paper treats propagation of transient waves in nonstationary media, which has many applications in, for example, 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 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's functions technique. More explicitly, the imbedding equation for the reflection kernel and the Green's functions (propagator kernels) equations are derived. Special attention is paid to the problem of nonstationary characteristics. A few numerical examples illustrate this problem. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Physics
volume
37
issue
5
pages
2229 - 2252
publisher
American Institute of Physics
external identifiers
  • scopus:0030527536
ISSN
0022-2488
DOI
10.1063/1.531506
language
English
LU publication?
yes
id
2fa863d0-4bc6-46e2-a3e0-3fa40e6bb481 (old id 143324)
date added to LUP
2007-07-11 11:07:20
date last changed
2017-01-01 07:26:19
@article{2fa863d0-4bc6-46e2-a3e0-3fa40e6bb481,
  abstract     = {This paper treats propagation of transient waves in nonstationary media, which has many applications in, for example, 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 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's functions technique. More explicitly, the imbedding equation for the reflection kernel and the Green's functions (propagator kernels) equations are derived. Special attention is paid to the problem of nonstationary characteristics. A few numerical examples illustrate this problem.},
  author       = {Åberg, Ingegerd and Kristensson, Gerhard and Wall, David J. N.},
  issn         = {0022-2488},
  language     = {eng},
  number       = {5},
  pages        = {2229--2252},
  publisher    = {American Institute of Physics},
  series       = {Journal of Mathematical Physics},
  title        = {Transient waves in nonstationary media},
  url          = {http://dx.doi.org/10.1063/1.531506},
  volume       = {37},
  year         = {1996},
}