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Numerical study of the Davey-Stewartson system

Published online by Cambridge University Press:  15 December 2004

Christophe Besse ,
Norbert J. Mauser  and
Hans Peter Stimming
Christophe Besse
Affiliation:
Laboratoire MIP, UMR 5640, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France. besse@mip.ups-tlse.fr.
Norbert J. Mauser
Affiliation:
Wolfgang Pauli Institute c/o Fakultät f. Math., Universität Wien, Nordbergstr. 15, A 1090 Wien, Austria. mauser@courant.nyu.edu.
Hans Peter Stimming
Affiliation:
Wolfgang Pauli Institute, Wien and ENS Lyon, France. hans.peter.stimming@univie.ac.at.
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Abstract

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.

Keywords

Nonlinear Schrödinger type equationsurface wavetime-splitting spectral schemefinite time blowup.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 6 , November 2004 , pp. 1035 - 1054
Copyright
© EDP Sciences, SMAI, 2004

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