Geodesic
Exact method for solving nonstationary stochastic wave problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 3, pp. 390-395 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method is proposed for statistic modeling of pulsed signals scattering by layered media with stochastic inhomogeneities. Computation scheme is stable and corresponds to exact weak solution to stochastic wave equation. This method is applied to acoustic studies in ocean. 
@article{ZVMMF_2013_53_3_a7,
     author = {O. E. Gulin and I. O. Yaroshchuk},
     title = {Exact method for solving nonstationary stochastic wave problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {390--395},
     year = {2013},
     volume = {53},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a7/}
}
TY  - JOUR
AU  - O. E. Gulin
AU  - I. O. Yaroshchuk
TI  - Exact method for solving nonstationary stochastic wave problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 390
EP  - 395
VL  - 53
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a7/
LA  - ru
ID  - ZVMMF_2013_53_3_a7
ER  - 
%0 Journal Article
%A O. E. Gulin
%A I. O. Yaroshchuk
%T Exact method for solving nonstationary stochastic wave problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 390-395
%V 53
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a7/
%G ru
%F ZVMMF_2013_53_3_a7
O. E. Gulin; I. O. Yaroshchuk. Exact method for solving nonstationary stochastic wave problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 3, pp. 390-395. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a7/

[1] Barridge R., Papanicolaou G., White B., “Statistics for pulse reflection from a randomly layered medium”, SIAM J. Appl. Math., 47:1 (1987), 146–168 | DOI | MR

[2] Klyatskin V. I., Saichev A. I., “Statisticheskaya i dinamicheskaya lokalizatsiya ploskikh voln v khaoticheski sloistykh sredakh”, Uspekhi fiz. nauk, 162:3 (1992), 161–194 | DOI

[3] Shevtsov B. M., Nestatsionarnye otrazheniya v sluchainykh i khaoticheskikh sredakh, Nauka, M., 2008

[4] Klyatskin V. I., Stokhasticheskie uravneniya. Teoriya i ee prilozheniya k akustike, gidrodinamike i radiofizike, v. 2, Fizmatlit, M., 2008

[5] Yaroschuk I. O., Statisticheskoe modelirovanie sluchainykh volnovykh polei v sloistykh sredakh, avtoref. dis. ... dokt. fiz.-matem. nauk, Tikhook. okeanol. in-t im. V. I. Ilicheva TOI DVO RAN, Vladivostok, 2003

[6] Gulin O.É., Yaroshchuk I. O., “Statistical modeling of the backscattered field in a one-dimensional non-stationary stochastic problem”, J. Waves in Random Media, 11 (2001), 413–423 | DOI | Zbl

[7] Gulin O.É., Yaroshchuk I. O., “On some approximations for non-stationary problem of the acoustical pulse scattering by a random medium”, J. Comput. Acoust., 12:1 (2004), 23–35 | DOI | MR | Zbl

[8] Gulin O. E., Temchenko V. V., “Analitiko-chislennyi metod modelirovaniya nestatsionarnykh volnovykh polei v sloistykh sredakh”, Zh. vychisl. matem. i matem. fiz., 37:4 (1997), 499–504 | MR | Zbl

[9] Wright D. J., “The digital simulation of stochastic differentional equations”, Trans. IEEE, AS-19:1 (1974), 75–76 | Zbl

[10] Jensen F. B., Kuperman W. A., Porter M. B., Schmidt H., Computational ocean acoustics, Springer, New-York, 2011