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• W2123988768 abstract "Plane wave solutions to the cubic nonlinear Schrodinger equation on a torus have recently been shown to behave orbitally stable. Under generic perturbations of the initial data that are small in a high-order Sobolev norm, plane waves are stable over long times that extend to arbitrary negative powers of the smallness parameter. The present paper studies the question as to whether numerical discretizations by the split-step Fourier method inherit such a generic long-time stability property. This can indeed be shown under a condition of linear stability and a non-resonance condition. They can both be verified if the time step-size is restricted by a CFL condition in the case of a constant plane wave. The proof first uses a Hamiltonian reduction and transformation and then modulated Fourier expansions in time. It provides detailed insight into the structure of the numerical solution." @default.
• W2123988768 created "2016-06-24" @default.
• W2123988768 creator A5045956945 @default.
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• W2123988768 date "2013-06-04" @default.
• W2123988768 modified "2023-09-27" @default.
• W2123988768 title "Plane wave stability of the split-step Fourier method for the nonlinear Schrodinger equation" @default.
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• W2123988768 hasPublicationYear "2013" @default.
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