# 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

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topBesse, 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 -

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