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AbstractUsing a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. 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 of the fractional nonlinear Schrödinger equation.
CitationKlein C, Sparber C, Markowich P (2014) Numerical study of fractional nonlinear Schrodinger equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470: 20140364–20140364. Available: http://dx.doi.org/10.1098/rspa.2014.0364.
SponsorsC.S. acknowledges support by the NSF through grant no. DMS-1161580. Additional support was provided through the NSF research network Ki-Net.
PublisherThe Royal Society
PubMed Central IDPMC4241009
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