Raman laser : mathematical and numerical analysis of a model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 3, p. 457-475

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.

DOI : https://doi.org/10.1051/m2an:2004022
Classification:  65L10,  65L20
Keywords: optical device, Raman gain, Poisson system, integro-differential equations
@article{M2AN_2004__38_3_457_0,
author = {Castella, Fran\c cois 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {38},
number = {3},
year = {2004},
pages = {457-475},
doi = {10.1051/m2an:2004022},
zbl = {1078.78012},
mrnumber = {2075755},
language = {en},
url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 3, pp. 457-475. doi : 10.1051/m2an:2004022. http://www.numdam.org/item/M2AN_2004__38_3_457_0/

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