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Solitary waves in nematic liquid crystals

Journal Article


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Abstract


  • We study soliton solutions of a two-dimensional nonlocal NLS equation of Hartree-type with

    a Bessel potential kernel. The equation models laser propagation in nematic liquid crystals.

    Motivated by the experimental observation of spatially localized beams, see [CPA03], we show

    existence, stability, regularity, and radial symmetry of energy minimizing soliton solutions in

    R2. We also give theoretical lower bounds for the L2−norm (power) of these solitons, and show

    that small L2−norm initial conditions lead to decaying solutions. We also present numerical

    computations of radial soliton solutions. These solutions exhibit the properties expected by the

    infinite plane theory, although we also see some finite (computational) domain effects, especially

    solutions with arbitrarily small power.

Publication Date


  • 2014

Citation


  • Panayotaros, P. & Marchant, T. R. (2014). Solitary waves in nematic liquid crystals. Physica D: Nonlinear Phenomena, 268 106-117.

Scopus Eid


  • 2-s2.0-84891608022

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2925&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1916

Number Of Pages


  • 11

Start Page


  • 106

End Page


  • 117

Volume


  • 268

Place Of Publication


  • http://www.sciencedirect.com/science/article/pii/S0167278913002935

Abstract


  • We study soliton solutions of a two-dimensional nonlocal NLS equation of Hartree-type with

    a Bessel potential kernel. The equation models laser propagation in nematic liquid crystals.

    Motivated by the experimental observation of spatially localized beams, see [CPA03], we show

    existence, stability, regularity, and radial symmetry of energy minimizing soliton solutions in

    R2. We also give theoretical lower bounds for the L2−norm (power) of these solitons, and show

    that small L2−norm initial conditions lead to decaying solutions. We also present numerical

    computations of radial soliton solutions. These solutions exhibit the properties expected by the

    infinite plane theory, although we also see some finite (computational) domain effects, especially

    solutions with arbitrarily small power.

Publication Date


  • 2014

Citation


  • Panayotaros, P. & Marchant, T. R. (2014). Solitary waves in nematic liquid crystals. Physica D: Nonlinear Phenomena, 268 106-117.

Scopus Eid


  • 2-s2.0-84891608022

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2925&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1916

Number Of Pages


  • 11

Start Page


  • 106

End Page


  • 117

Volume


  • 268

Place Of Publication


  • http://www.sciencedirect.com/science/article/pii/S0167278913002935