In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.
Mots-clés : optical device, Raman gain, Poisson system, integro-differential equations
@article{M2AN_2004__38_3_457_0,
author = {Castella, Fran\c{c}ois and Chartier, Philippe and Faou, Erwan and Bayart, Dominique and Leplingard, Florence and Martinelli, Catherine},
title = {Raman laser : mathematical and numerical analysis of a model},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {457--475},
publisher = {EDP-Sciences},
volume = {38},
number = {3},
year = {2004},
doi = {10.1051/m2an:2004022},
mrnumber = {2075755},
zbl = {1078.78012},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2004022/}
}
TY - JOUR AU - Castella, François AU - Chartier, Philippe AU - Faou, Erwan AU - Bayart, Dominique AU - Leplingard, Florence AU - Martinelli, Catherine TI - Raman laser : mathematical and numerical analysis of a model JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 457 EP - 475 VL - 38 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004022/ DO - 10.1051/m2an:2004022 LA - en ID - M2AN_2004__38_3_457_0 ER -
%0 Journal Article %A Castella, François %A Chartier, Philippe %A Faou, Erwan %A Bayart, Dominique %A Leplingard, Florence %A Martinelli, Catherine %T Raman laser : mathematical and numerical analysis of a model %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 457-475 %V 38 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004022/ %R 10.1051/m2an:2004022 %G en %F M2AN_2004__38_3_457_0
Castella, François; Chartier, Philippe; Faou, Erwan; Bayart, Dominique; Leplingard, Florence; Martinelli, Catherine. Raman laser : mathematical and numerical analysis of a model. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 3, pp. 457-475. doi : 10.1051/m2an:2004022. http://www.numdam.org/articles/10.1051/m2an:2004022/
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