Transient waves in nonstationary media
(1996) In Journal of Mathematical Physics 37(5). p.22292252 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, firstorder 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, firstorder 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
 00222488
 DOI
 10.1063/1.531506
 language
 English
 LU publication?
 yes
 id
 2fa863d04bc646e2a3e03fa40e6bb481 (old id 143324)
 date added to LUP
 20160401 17:10:33
 date last changed
 20220129 00:55:24
@article{2fa863d04bc646e2a3e03fa40e6bb481, 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, firstorder 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 = {{00222488}}, language = {{eng}}, number = {{5}}, pages = {{22292252}}, 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}}, }