Transient waves in nonstationary media
(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:
https://lup.lub.lu.se/record/143324
- author
- Åberg, Ingegerd ; Kristensson, Gerhard LU and Wall, David J. N.
- organization
- publishing date
- 1996
- 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 (AIP)
- 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
- 2016-04-01 17:10:33
- date last changed
- 2022-01-29 00:55:24
@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 (AIP)}},
series = {{Journal of Mathematical Physics}},
title = {{Transient waves in nonstationary media}},
url = {{http://dx.doi.org/10.1063/1.531506}},
doi = {{10.1063/1.531506}},
volume = {{37}},
year = {{1996}},
}