Raman laser: mathematical and numerical analysis of a model

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...

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Veröffentlicht in:	ESAIM. Mathematical modelling and numerical analysis 2004-05, Vol.38 (3), p.457-475
Hauptverfasser:	Castella, François, Chartier, Philippe, Faou, Erwan, Bayart, Dominique, Leplingard, Florence, Martinelli, Catherine
Format:	Artikel
Sprache:	eng
Schlagworte:	65L10 65L20 Approximation Boundary conditions Exact sciences and technology integro-differential equations Lasers Mathematics Numerical analysis Numerical analysis. Scientific computation Optical device Ordinary differential equations Poisson system Raman gain Sciences and techniques of general use
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Beschreibung
Zusammenfassung:	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.
ISSN:	0764-583X 1290-3841
DOI:	10.1051/m2an:2004022