Numerical study of the Davey-Stewartson system

Christophe Besse; Norbert J. Mauser; Hans Peter Stimming

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 6, page 1035-1054
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Besse, Christophe, Mauser, Norbert J., and Stimming, Hans Peter. "Numerical study of the Davey-Stewartson system." ESAIM: Mathematical Modelling and Numerical Analysis 38.6 (2010): 1035-1054. <http://eudml.org/doc/194246>.

@article{Besse2010,
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. },
author = {Besse, Christophe, Mauser, Norbert J., Stimming, Hans Peter},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonlinear Schrödinger type equation; surface wave; time-splitting spectral scheme; finite time blowup.; nonlinear Schrödinger type equation; surface waves; time splitting spectral method; blow up},
language = {eng},
month = {3},
number = {6},
pages = {1035-1054},
publisher = {EDP Sciences},
title = {Numerical study of the Davey-Stewartson system},
url = {http://eudml.org/doc/194246},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Besse, Christophe
AU - Mauser, Norbert J.
AU - Stimming, Hans Peter
TI - Numerical study of the Davey-Stewartson system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 6
SP - 1035
EP - 1054
AB - 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.
LA - eng
KW - Nonlinear Schrödinger type equation; surface wave; time-splitting spectral scheme; finite time blowup.; nonlinear Schrödinger type equation; surface waves; time splitting spectral method; blow up
UR - http://eudml.org/doc/194246
ER -

References

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