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poisson system

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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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
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 38 / Issue 3 / May 2004

Published online by Cambridge University Press:

15 June 2004, pp. 457-475

Print publication:

May 2004
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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.