2014/04/30 by C. Klein, C. Sparber, P. Markowich · 1 citation
Mathematics · #math.AP
paper · pdf · doi:10.1098/rspa.2014.0364
minor changes
arxiv created 2014/05/04 · arxiv updated 2015/06/19
Using a Fourier spectral method, we provide a detailed numerically investigation of dispersive Schrödinger type equations involving a fractional Laplacian. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be computed in one spatial dimension, only. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states, and the long time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions to the fractional nonlinear Schrödinger equation.