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Purely Kerr nonlinear model admitting flat-top solitons.

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    Researchers model flat-top solitons using self-repulsive cubic nonlinearity, a novel approach for optics and Bose-Einstein condensates. Stable fundamental solitons and multipoles are found, with alternating stability for higher-order structures.

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    Area of Science:

    • Nonlinear physics
    • Soliton theory
    • Optical physics
    • Bose-Einstein condensates

    Background:

    • Previous research on solitons primarily utilized competing nonlinearities.
    • Flat-top solitons were not previously achievable with self-repulsive cubic nonlinearity alone.

    Purpose of the Study:

    • To develop and analyze one- and two-dimensional models of media with spatially modulated self-repulsive cubic nonlinearity.
    • To investigate the existence and stability of various types of flat-top solitons, including fundamental solitons, multipoles, and vortices.
    • To explore potential applications in optics and Bose-Einstein condensates.

    Main Methods:

    • Development of 1D and 2D mathematical models incorporating spatial modulation of cubic nonlinearity.
    • Derivation of exact analytical solutions for 1D flat-top solitons.
    • Application of the Thomas-Fermi approximation for predicting soliton families.
    • Linear-stability analysis and direct numerical simulations to assess soliton stability.

    Main Results:

    • Demonstrated the existence of flat-top solitons (fundamental, multipoles, vortices) in media with self-repulsive cubic nonlinearity.
    • Obtained an exact analytical solution for stable 1D flat-top solitons.
    • Identified completely stable fundamental solitons and 1D multipoles (k=1, 2) and 2D vortices (m=1).
    • Revealed alternating stripes of stability and instability for higher-order multipoles (k≥3) and vortices (m≥2).

    Conclusions:

    • The study successfully establishes a new framework for generating flat-top solitons using self-repulsive cubic nonlinearity.
    • The findings offer precise analytical and approximate methods for predicting and understanding these solitons.
    • The identified stability properties provide crucial insights for experimental realization in optics and Bose-Einstein condensates.