Collapse arrest and soliton stabilization in nonlocal nonlinear media

2002/10/24 by Ole Bang, Wieslaw Krolikowski, Wiesław Królikowski +3 · 3 citations
Physics and Astronomy · #Advanced Fiber Laser Technologies #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.1103/physreve.66.046619

openalex publication_date 2002/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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 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.

Citations

• Bose-Einstein condensation with magnetic dipole-dipole forces

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• Measurement of the self-induced waveguide of a solitonlike optical beam in a nematic liquid crystal
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