Numerical study of fractional nonlinear Schrodinger equations

Christian Klein, Christof Sparber, Peter A. Markowich

Research output: Contribution to journalArticlepeer-review

47 Scopus citations

Abstract

Using 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.
Original languageEnglish (US)
Pages (from-to)20140364
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume470
Issue number2172
DOIs
StatePublished - Oct 8 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: C.S. acknowledges support by the NSF through grant no. DMS-1161580. Additional support was provided through the NSF research network Ki-Net.

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