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arXiv · 1404.6262

Numerical study of fractional Nonlinear Schrödinger equations

C. Klein·C. Sparber·P. Markowich
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Abstract

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.

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C. Klein, C. Sparber, P. Markowich. 2014-05-04. Numerical study of fractional Nonlinear Schrödinger equations. https://doi.org/10.1098/rspa.2014.0364

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