Collapse arrest and soliton stabilization in nonlocal nonlinear media

Publication: Research - peer-reviewJournal article – Annual report year: 2002

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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
StatePublished - 2002
Peer-reviewedYes

Bibliographical note

Copyright (2002) American Physical Society

CitationsWeb of Science® Times Cited: 260

Keywords

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