Geodesic
Numerical study of self-focusing solutions to the Schrödinger-Debye system
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 1, pp. 35-55

Voir la notice de l'article provenant de la source Numdam

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.

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.

Classification : 35Q55, 35Q60, 65M06, 65M70, 78A60
Keywords: nonlinear optics, Schrödinger-like equations, relaxation method, split-step method, self-focusing 
@article{M2AN_2001__35_1_35_0,
     author = {Besse, Christophe and Bid\'egaray, Brigitte},
     title = {Numerical study of self-focusing solutions to the {Schr\"odinger-Debye} system},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {35--55},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {1},
     year = {2001},
     mrnumber = {1811980},
     zbl = {0979.65086},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_35_0/}
}
TY  - JOUR
AU  - Besse, Christophe
AU  - Bidégaray, Brigitte
TI  - Numerical study of self-focusing solutions to the Schrödinger-Debye system
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2001
SP  - 35
EP  - 55
VL  - 35
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_35_0/
LA  - en
ID  - M2AN_2001__35_1_35_0
ER  - 
%0 Journal Article
%A Besse, Christophe
%A Bidégaray, Brigitte
%T Numerical study of self-focusing solutions to the Schrödinger-Debye system
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2001
%P 35-55
%V 35
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_35_0/
%G en
%F M2AN_2001__35_1_35_0
Besse, Christophe; Bidégaray, Brigitte. Numerical study of self-focusing solutions to the Schrödinger-Debye system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 1, pp. 35-55. http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_35_0/