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    Numerical study of fractional nonlinear Schrödinger equations

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    Date
    2014-10
    Author
    KLEIN, C.
    SPARBER, C.
    Markowich, P.
    Publisher
    The Royal Society
    Metadata
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    Abstract
    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
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    Type
    Article
    Date available in INDIGO
    2016-01-23T10:30:17Z
    URI
    http://hdl.handle.net/10027/20038
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    • Publications - Mathematics, Statistics, and Computer Science

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