The “interaction picture” (IP) method is a very promising alternative to Split-Step methods for solving certain type of partial differential equations such as the nonlinear Schrödinger equation used in the simulation of wave propagation in optical fibers. The method exhibits interesting convergence properties and is likely to provide more accurate numerical results than cost comparable Split-Step methods such as the Symmetric Split-Step method. In this work we investigate in detail the numerical properties of the IP method and carry out a precise comparison between the IP method and the Symmetric Split-Step method.
DOI : 10.1051/m2an/2015060
Mots clés : Interaction picture method, symmetric Split-Step method, Runge−Kutta method, nonlinear optics, nonlinear Schrödinger equation
@article{M2AN_2016__50_4_945_0,
author = {Balac, St\'ephane and Fernandez, Arnaud and Mah\'e, Fabrice and M\'ehats, Florian and Texier-Picard, Rozenn},
title = {The {Interaction} {Picture} method for solving the generalized nonlinear {Schr\"odinger} equation in optics},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {945--964},
publisher = {EDP-Sciences},
volume = {50},
number = {4},
year = {2016},
doi = {10.1051/m2an/2015060},
zbl = {1401.78014},
mrnumber = {3521707},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2015060/}
}
TY - JOUR AU - Balac, Stéphane AU - Fernandez, Arnaud AU - Mahé, Fabrice AU - Méhats, Florian AU - Texier-Picard, Rozenn TI - The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 945 EP - 964 VL - 50 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015060/ DO - 10.1051/m2an/2015060 LA - en ID - M2AN_2016__50_4_945_0 ER -
%0 Journal Article %A Balac, Stéphane %A Fernandez, Arnaud %A Mahé, Fabrice %A Méhats, Florian %A Texier-Picard, Rozenn %T The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 945-964 %V 50 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015060/ %R 10.1051/m2an/2015060 %G en %F M2AN_2016__50_4_945_0
Balac, Stéphane; Fernandez, Arnaud; Mahé, Fabrice; Méhats, Florian; Texier-Picard, Rozenn. The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 945-964. doi : 10.1051/m2an/2015060. http://www.numdam.org/articles/10.1051/m2an/2015060/
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