Subcritical localization in the discrete nonlinear Schrödinger equation with arbitrary power nonlinearity

O. Bang, J. Juul Rasmussen, P.L. Christiansen

    Research output: Contribution to journalJournal articleResearch

    Abstract

    Discretizing the continuous nonlinear Schrodinger equation with arbitrary power nonlinearity influences the time evolution of its ground state solitary solution. In the subcritical case, for grid resolutions above a certain transition value, depending on the degree of nonlinearity, the solution will oscillate smoothly with a frequency and amplitude that depend on both the resolution and the degree of nonlinearity. Thus in this region the discrete system will give a good reproduction of the dynamics in the continuum one. However, when the discretization gets too coarse the solution will become localized in finite time, although the degree of nonlinearity is subcritical. Thus in this region the discrete system cannot reproduce the stable solitary solution found in the continuum system. Numerical studies of the phenomenon are performed and a variational approach is used to give a qualitative explanation of the dynamics in the discrete system.
    Original languageEnglish
    JournalNonlinearity
    Volume7
    Issue number1
    Pages (from-to)205-218
    ISSN0951-7715
    DOIs
    Publication statusPublished - 1994

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