Numerical study of the Davey-Stewartson system

Christophe Besse; Norbert J. Mauser; Hans Peter Stimming

Displaying similar documents to “Numerical study of the Davey-Stewartson system”

Numerical study of the Davey-Stewartson system

Christophe Besse, Norbert J. Mauser, Hans Peter Stimming (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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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...

Geometric optics and instability for NLS and Davey-Stewartson models

Rémi Carles, Eric Dumas, Christof Sparber (2012)

Journal of the European Mathematical Society

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We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrödinger equations with Gauge invariant power-law nonlinearities and nonlocal perturbations. The model includes the Davey-Stewartson system in its elliptic-elliptic and hyperbolic-elliptic variants. Our analysis reveals a new localization phenomenon for nonlocal perturbations in the high frequency regime and allows us to infer strong instability results on the Cauchy problem in negative...

Multicanonical systems of elliptic surfaces in small characteristics

Toshiyuki Katsura (1995)

Compositio Mathematica

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Remarks on the Existence of Many Solutions of Certain Nonlinear Elliptic Equations

Edward N. Dancer, Shusen Yan (2007)

Bollettino dell'Unione Matematica Italiana

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We show how a change of variable and peak solution methods can be used to prove that a number of nonlinear elliptic partial differential equations have many solutions.

Spectral Methods for Exterior Elliptic Problems.

C. Canuto, S.I. Hariharan, L. Lustman (1985)

Numerische Mathematik

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Configurations of In Fibers on Elliptic K 3 Surface.

Rick Miranda, Ulf Persson (1989)

Mathematische Zeitschrift

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Weierstrass elliptic solutions to a Zakharov equation in plasmas with power law nonlinearity

A. El Achab (2015)

Applicationes Mathematicae

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In this paper, travelling wave solutions for the Zakharov equation in plasmas with power law nonlinearity are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given.

On some elliptic boundary-value problems with discontinuous nonlinearities

Giovanni Anello (2005)

Annales Polonici Mathematici

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We establish two existence results for elliptic boundary-value problems with discontinuous nonlinearities. One of them concerns implicit elliptic equations of the form ψ(-Δu) = f(x,u). We emphasize that our assumptions permit the nonlinear term f to be discontinuous with respect to the second variable at each point.