| Issue |
ESAIM: M2AN
Volume 38, Number 6, November-December 2004
|
|
|---|---|---|
| Page(s) | 1035 - 1054 | |
| DOI | https://doi.org/10.1051/m2an:2004049 | |
| Published online | 15 December 2004 | |
Numerical study of the Davey-Stewartson system
1
Laboratoire MIP, UMR 5640, Université Paul Sabatier,
118 Route de Narbonne, 31062 Toulouse Cedex, France. besse@mip.ups-tlse.fr.
2
Wolfgang Pauli Institute c/o Fakultät f. Math.,
Universität Wien,
Nordbergstr. 15, A 1090 Wien, Austria. mauser@courant.nyu.edu.
3
Wolfgang Pauli Institute, Wien and ENS Lyon, France.
hans.peter.stimming@univie.ac.at.
Received:
5
May
2004
Revised:
22
September
2004
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.
Mathematics Subject Classification: 35Q55 / 65M12 / 65M70 / 76B45
Key words: Nonlinear Schrödinger type equation / surface wave / time-splitting spectral scheme / finite time blowup.
© EDP Sciences, SMAI, 2004
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