Geodesic
Numerical study of the Davey-Stewartson system
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 6, pp. 1035-1054

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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 : 10.1051/m2an:2004049
Classification : 35Q55, 65M12, 65M70, 76B45
Keywords: nonlinear Schrödinger type equation, surface wave, time-splitting spectral scheme, finite time blowup 
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     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 },
     pages = {1035--1054},
     publisher = {EDP-Sciences},
     volume = {38},
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     year = {2004},
     doi = {10.1051/m2an:2004049},
     mrnumber = {2108943},
     zbl = {1080.65095},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004049/}
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Besse, Christophe; Mauser, Norbert J.; Stimming, Hans Peter. Numerical study of the Davey-Stewartson system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 6, pp. 1035-1054. doi: 10.1051/m2an:2004049

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