Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise

Peter Leth Christiansen, Yuri Borisovich Gaididei, Kim Rasmussen, Magnus Johansson, Irina I. Yakimenko

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    Abstract

    We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schrodinger equation (NLS). Using a collective approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead in an exponentially decreasing width of the solution in the long-time limit. We also find that a sufficiently large noise variance may cause an initially localized distribution to spread instead of contracting, and that the critical variance necessary to cause dispersion will for small damping be the same as for the undamped system.
    Original languageEnglish
    JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
    Volume54
    Issue number1
    Pages (from-to)924-930
    ISSN1063-651X
    DOIs
    Publication statusPublished - 1996

    Bibliographical note

    Copyright (1996) American Physical Society.

    Keywords

    • SOLITONS

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