Numerical study of self-focusing solutions to the Schrödinger-Debye system
Christophe Besse; Brigitte Bidégaray
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 35, Issue: 1, page 35-55
- ISSN: 0764-583X
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topBesse, Christophe, and Bidégaray, Brigitte. "Numerical study of self-focusing solutions to the Schrödinger-Debye system." ESAIM: Mathematical Modelling and Numerical Analysis 35.1 (2010): 35-55. <http://eudml.org/doc/197428>.
@article{Besse2010,
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.
},
author = {Besse, Christophe, Bidégaray, Brigitte},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonlinear optics; Schrödinger-like equations; relaxation method;
split-step method; self-focusing.; self-focusing solutions; Schrödinger-Debye system; nonlinear optics; blow-up solutions; relaxation scheme; split-step method},
language = {eng},
month = {3},
number = {1},
pages = {35-55},
publisher = {EDP Sciences},
title = {Numerical study of self-focusing solutions to the Schrödinger-Debye system},
url = {http://eudml.org/doc/197428},
volume = {35},
year = {2010},
}
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
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 1
SP - 35
EP - 55
AB -
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.
LA - eng
KW - Nonlinear optics; Schrödinger-like equations; relaxation method;
split-step method; self-focusing.; self-focusing solutions; Schrödinger-Debye system; nonlinear optics; blow-up solutions; relaxation scheme; split-step method
UR - http://eudml.org/doc/197428
ER -
References
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