Numerical study of self-focusing solutions to the Schrödinger-Debye system
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 1, pp. 35-55.

Dans cet article nous mettons en œuvre différents schémas numériques pour simuler les équations de Schrödinger-Debye qui sont issues de l'optique non linéaire. Comme l'existence de solutions qui explosent en temps fini est un problème ouvert, nous essayons de calculer de telles solutions. On prouve la convergence des méthodes et les résultats numériques semblent en effet montrer qu'au moins pour de petits temps de retard il peut exister des solutions qui explosent en temps fini.

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.

Classification : 35Q55, 35Q60, 65M06, 65M70, 78A60
Mots-clés : nonlinear optics, Schrödinger-like equations, relaxation method, split-step method, self-focusing 
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Besse, Christophe; Bidégaray, Brigitte. Numerical study of self-focusing solutions to the Schrödinger-Debye system. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 1, pp. 35-55. http://www.numdam.org/item/M2AN_2001__35_1_35_0/

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