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

Christophe Besse; Brigitte Bidégaray

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 1, page 35-55
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Besse, Christophe, and Bidégaray, Brigitte. "Numerical study of self-focusing solutions to the Schrödinger-Debye system." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.1 (2001): 35-55. <http://eudml.org/doc/194044>.

@article{Besse2001,
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 - Modélisation Mathématique et Analyse Numérique},
keywords = {nonlinear optics; Schrödinger-like equations; relaxation method; split-step method; self-focusing; self-focusing solutions; Schrödinger-Debye system; blow-up solutions; relaxation scheme},
language = {eng},
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/194044},
volume = {35},
year = {2001},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2001
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; blow-up solutions; relaxation scheme
UR - http://eudml.org/doc/194044
ER -

References

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