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AbstractNonlinear dispersive partial differential equations such as the nonlinear Schrödinger equations can have solutions that blow up. We numerically study the long time behavior and potential blow-up of solutions to the focusing Davey-Stewartson II equation by analyzing perturbations of the lump and the Ozawa solutions. It is shown in this way that both are unstable to blow-up and dispersion, and that blow-up in the Ozawa solution is generic.
CitationKlein C, Muite B, Roidot K (2013) Numerical study of blow-up in the Davey-Stewartson system. Discrete and Continuous Dynamical Systems - Series B 18: 1361–1387. Available: http://dx.doi.org/10.3934/dcdsb.2013.18.1361.