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

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 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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