Journal
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
Volume 38, Issue 6, Pages 1035-1054Publisher
E D P SCIENCES
DOI: 10.1051/m2an:2004049
Keywords
nonlinear Schrodinger type equation; surface wave; time-splitting spectral scheme; finite time blowup
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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.
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