Collapse arrest and soliton stabilization in nonlocal nonlinear media

Ole Bang, Wieslaw Krolikowski, John Wyller, Jens Juul Rasmussen

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    Abstract

    We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric and have a positive definite Fourier spectrum, but can otherwise be of completely arbitrary shape and degree of nonlocality. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.
    Original languageEnglish
    JournalPhysical Review E. Statistical, Nonlinear, and Soft Matter Physics
    Volume66
    Issue number4
    Pages (from-to)046619
    Number of pages5
    ISSN1063-651X
    DOIs
    Publication statusPublished - 2002

    Bibliographical note

    Copyright (2002) American Physical Society

    Keywords

    • SYSTEMS
    • GASES
    • LOCALIZATION
    • WAVE COLLAPSE
    • SCHRODINGER-EQUATION
    • LIGHT BEAMS
    • STABILITY
    • DYNAMICS

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