We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media.

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Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media

We investigate analytically and numerically the interactions of dark solitons under competing nonlocal cubic and local quintic nonlinearities. It is shown that the self-defocusing quintic nonlinearity will strengthen the attractive interaction and decrease the relative distance between solitons, whereas the self-focusing quintic nonlinearity will enhance the repulsive interaction and increase soliton separation. We demonstrate these results by approximate variational approach and direct numerical simulation.

Interactions of nonlocal dark solitons under competing cubic–quintic nonlinearities

We reveal a controllable manipulation of anomalous interactions between Airy beams in nonlocal nematic liquid crystals numerically. With the help of an in-phase fundamental Gaussian beam, attraction between in-phase Airy beams can be suppressed or become a repulsive one to each other; whereas the attraction can be strengthened when the Gaussian beam is out-of-phase. In contrast to the repulsive interaction in local media, stationary bound states of breathing Airy soliton pairs are found in nematic liquid crystals.

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Control on the anomalous interactions of Airy beams in nematic liquid crystals.

Theoretical and experimental results on optical ring dark solitary waves are presented, emphasizing the interplay between initial dark beam contrast, phase-shift magnitude, background-beam intensity and saturation of the nonlinearity are presented. The results are found to confirm qualitatively the existing analytical theory and are in agreement with the numerical simulations carried out.

Ring dark solitary waves: experiment versus theory

This paper is concerned with the numerical integration in time of nonlinear Schrodinger equations using different methods preserving the energy or a discrete analog of it. The Crank-Nicolson method is a well known method of order 2 but is fully implicit and one may prefer a linearly implicit method like the relaxation method introduced in [10] for the cubic nonlinear Schr{o}dinger equation. This method is also an energy preserving method and numerical simulations have shown that its order is 2. In this paper we give a rigorous proof of the order of this relaxation method and propose a generalized version that allows to deal with general power law nonlinearites. Numerical simulations for different physical models show the efficiency of these methods.

Wei Chen

Papers

Interactions of nonlocal dark solitons under competing cubic–quintic nonlinearities

Polarized vector dark solitons in nonlocal Kerr-type self-defocusing media

Stabilization of two-dimensional dark and anti-dark solitons in a nonlocal media

Analytical theory of two-dimensional ring dark soliton in nonlocal nonlinear media

Erratum: Polarized vector dark solitons in nonlocal Kerr-type self-defocusing media [Phys. Rev. A 87 , 013809 (2013)]