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EN
We investigate exact soliton solutions with nonlinear chirp for the coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity, self-steepening, self-frequency shift and four-wave mixing. The model governs the femtosecond pulse propagation in birefringent fibers. We introduce a new ansatz to obtain the nonlinear chirp associated with the propagating soliton pulses. New chirped soliton pair solutions with non-trivial chirping are found for the coupled nonlinear equations, illustrating the potentially rich set of solitonic pulse solutions of the model with higher-order effects. The solutions comprise two types of bright-W-shaped and bright-bright soliton pairs as well as kink and anti-kink pulses. Interestingly, the bright wave in the bright-W shaped soliton pairs possesses a platform underneath it, originating from the self-steepening and self-frequency shift effects. The corresponding chirp associated with each of these optical soliton pairs is also determined. It is shown that the nonlinear chirp is related to the pair intensity and determined by self-frequency shift and pause self-steepening. Parametric conditions for the existence and uniqueness of chirped solutions are given.
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Hyper-Solitons in Nematic Liquid Crystals

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EN
We study laser light propagation in a cell containing a liquid crystal in the nematic phase. We launch hyper-Gaussian beams and follow their behavior within the cell, in time and in three spatial dimensions, utilizing an appropriately developed theoretical model and a numerical procedure based on the fast Fourier transform. We demonstrate the formation of stable "hyper-soliton" breathers in a narrow region of beam intensities, for fixed other parameters. Hyper-solitons are similar in appearance and behavior to the usual solitons, formed by launching the usual Gaussian beams; however noticeable differences persist.
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Counterpropagating Matter Waves in Optical Lattices

88%
EN
An investigation of Bose-Einstein condensate in two-dimensional optical lattice potentials, formed by laser beams, is carried out. We are interested in the dynamics of Bose-Einstein condensate in a square optical lattice, where the periodic potential can lead to the stabilization of an otherwise unstable Bose-Einstein condensate. The behavior of Bose-Einstein condensate in optical lattices is described by the nonlinear Gross-Pitaevskii equation, which we treat numerically. By applying the Petviashvili iteration method, we demonstrate the existence of solitonic solutions in the case of counterpropagating matter waves, and analyze their stability.
EN
A review of work on the dynamical behavior of counterpropagating incoherent laser beams in photorefractive crystals is presented. Numerical study of counterpropagating beams of different type is carried out, in both space and time, using an appropriate theoretical model. The development of patterns in broad hyper-Gaussian counterpropagating beams in saturable Kerr-like media is investigated, by varying the width of beams. Rotational properties of counterpropagating mutually incoherent self-trapped vortex beams in optically induced fixed photonic lattices are also investigated numerically. One of the fundamental quantum mechanical phenomena is observed for the counterpropagating beams in photonic lattices, the tunneling of light from the first to the higher-order bands of the lattice band gap spectrum. The transfer of angular momentum from vortex beams to optically induced photonic lattices is also demonstrated. For the interacting beams it is found that the sum of angular momenta of counterpropagating components is not a conserved quantity, but the difference is. In the fixed lattices there is always a considerable loss of angular momentum.
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