Numerical study of fractional nonlinear Schrödinger equations
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Date
2014-10Author
KLEIN, C.
SPARBER, C.
Markowich, P.
Publisher
The Royal SocietyMetadata
Show full item recordAbstract
Using a Fourier spectral method, we provide a detailed numerical
investigation of dispersive Schr ̈odinger type equations involving a fractional
Laplacian in the one-dimensional case. By an appropriate choice of the dis-
persive exponent, both mass and energy sub- and supercritical regimes can be
identified. This allows us to study the possibility of finite time blow-up ver-
sus 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 of the fractional nonlinear Schr ̈odinger