We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing, elliptic-elliptic Davey-Stewartson systems and simultaneous blowup at multiple locations in the focusing elliptic-elliptic system. Also the modeling of exact soliton type solutions for the hyperbolic-elliptic (DS2) system is studied.
Mots clés : nonlinear Schrödinger type equation, surface wave, time-splitting spectral scheme, finite time blowup
@article{M2AN_2004__38_6_1035_0,
author = {Besse, Christophe and Mauser, Norbert J. and Stimming, Hans Peter},
title = {Numerical study of the {Davey-Stewartson} system},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1035--1054},
publisher = {EDP-Sciences},
volume = {38},
number = {6},
year = {2004},
doi = {10.1051/m2an:2004049},
mrnumber = {2108943},
zbl = {1080.65095},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2004049/}
}
TY - JOUR AU - Besse, Christophe AU - Mauser, Norbert J. AU - Stimming, Hans Peter TI - Numerical study of the Davey-Stewartson system JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 1035 EP - 1054 VL - 38 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004049/ DO - 10.1051/m2an:2004049 LA - en ID - M2AN_2004__38_6_1035_0 ER -
%0 Journal Article %A Besse, Christophe %A Mauser, Norbert J. %A Stimming, Hans Peter %T Numerical study of the Davey-Stewartson system %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 1035-1054 %V 38 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004049/ %R 10.1051/m2an:2004049 %G en %F M2AN_2004__38_6_1035_0
Besse, Christophe; Mauser, Norbert J.; Stimming, Hans Peter. Numerical study of the Davey-Stewartson system. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 1035-1054. doi : 10.1051/m2an:2004049. http://www.numdam.org/articles/10.1051/m2an:2004049/
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