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Numerical study of self-focusing solutions to the Schrödinger-Debye system

Published online by Cambridge University Press:  15 April 2002

Christophe Besse  and
Brigitte Bidégaray
Christophe Besse
Affiliation:
Laboratoire MIP, CNRS UMR 5640, Université Paul Sabatier, 118 route de Narbonne, Toulouse Cedex 4, France. (besse@mip.ups-tlse.fr; bidegara@mip.ups-tlse.fr)
Brigitte Bidégaray
Affiliation:
Laboratoire MIP, CNRS UMR 5640, Université Paul Sabatier, 118 route de Narbonne, Toulouse Cedex 4, France. (besse@mip.ups-tlse.fr; bidegara@mip.ups-tlse.fr)
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Abstract

In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.

Keywords

Nonlinear opticsSchrödinger-like equationsrelaxation methodsplit-step methodself-focusing.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 1 , January 2001 , pp. 35 - 55
Copyright
© EDP Sciences, SMAI, 2001

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