Numerical Study of Blowup in the Davey-Stewartson System

Details Numerical Study of Blowup in the Davey-Stewartson System Numerical Study of Blowup in the Davey-Stewartson System

2011-12-17

arxiv.org/abs/1112.4043v1

Mathematics

Analysis of PDEs

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Scientific paper

Nonlinear dispersive partial differential equations such as the nonlinear Schr\"odinger equations can have solutions that blow-up. We numerically study the long time behavior and potential blowup of solutions to the focusing Davey-Stewartson II equation by analyzing perturbations of the lump and the Ozawa exact solutions. It is shown in this way that the lump is unstable to both blowup and dispersion, and that blowup in the Ozawa solution is generic.

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