Numerical study of the Davey-Stewartson system
Laboratoire MIP, UMR 5640, Université Paul Sabatier,
118 Route de Narbonne, 31062 Toulouse Cedex, France. email@example.com.
2 Wolfgang Pauli Institute c/o Fakultät f. Math., Universität Wien, Nordbergstr. 15, A 1090 Wien, Austria. firstname.lastname@example.org.
3 Wolfgang Pauli Institute, Wien and ENS Lyon, France. email@example.com.
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