Numerical study of the Davey-Stewartson system
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 6, p. 1035-1054

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.

DOI : https://doi.org/10.1051/m2an:2004049
Classification:  35Q55,  65M12,  65M70,  76B45
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {6},
     year = {2004},
     pages = {1035-1054},
     doi = {10.1051/m2an:2004049},
     zbl = {1080.65095},
     mrnumber = {2108943},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2004__38_6_1035_0}
}
Besse, Christophe; Mauser, Norbert J.; Stimming, Hans Peter. Numerical study of the Davey-Stewartson system. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 6, pp. 1035-1054. doi : 10.1051/m2an:2004049. http://www.numdam.org/item/M2AN_2004__38_6_1035_0/

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