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Raman laser : mathematical and numerical analysis of a model

François Castella;  Philippe Chartier;  Erwan Faou;  Dominique Bayart;  Florence Leplingard;  Catherine Martinelli — 2004

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

Raman laser: mathematical and numerical analysis of a model

François Castella;  Philippe Chartier;  Erwan Faou;  Dominique Bayart;  Florence Leplingard;  Catherine Martinelli — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

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.

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