Nonlinear 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.
|Original language||English (US)|
|Number of pages||27|
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|State||Published - Apr 4 2013|