Collapse arrest and soliton stabilization in nonlocal nonlinear media

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

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    516 Citations (Scopus)


    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 Schrödinger 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
    Pages (from-to)5
    Number of pages1
    JournalPhysical Review E
    Issue number4
    Publication statusPublished - 24 Oct 2002


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