Robust soliton clusters in media with competing cubic and quintic nonlinearities
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Systematic results are reported for dynamics of circular patterns (“necklaces”), composed of fundamental solitons and carrying orbital angular momentum, in the two-dimensional model, which describes the propagation of light beams in bulk media combining self-focusing cubic and self-defocusing quintic nonlinearities. Semianalytical predictions for the existence of quasistable necklace structures are obtained on the basis of an effective interaction potential. Then, direct simulations are run. In the case when the initial pattern is far from an equilibrium size predicted by the potential, it cannot maintain its shape. However, a necklace with the initial shape close to the predicted equilibrium survives very long evolution, featuring persistent oscillations. The quasistable evolution is not essentially disturbed by a large noise component added to the initial configuration. Basic conclusions concerning the necklace dynamics in this model are qualitatively the same as in a recently studied one which combines quadratic and self-defocusing cubic nonlinearities. Thus, we infer that a combination of competing self-focusing and self-defocusing nonlinearities enhances the robustness not only of vortex solitons but also of vorticity-carrying necklace patterns.
CitationMihalache, D., Mazilu, D., Crasovan, L., Malomed, B., Lederer, F., Torner, L. Robust soliton clusters in media with competing cubic and quintic nonlinearities. "Physical review E, statistical physics, plasmas, fluids, and related interdisciplinary topics", Octubre 2003, vol. 68, p. 46612-46620.