Periodic solitons in optics

Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation

“…Similar oscillating solitons have been recently reported in Ref. [13] for a special case of so-called threshold nonlinearity. This oscillating regime in the soliton dynamics disappears when the soliton parameter w approaches the threshold curve of soliton stability.…”

“…Figures 5(a) and 5(b) show several characteristic examples of the soliton evolution for the eft'ective propagation constant cu(t) which is determined numerically as the first-order derivative of the soliton phase calculated at the pulse maximum. Each dependence corresponds to diferent values of the perturbation parameter a, and the results are in good agreement with the predictions of the analytical model (13) [see the trajectories on the phase plane shown in Fig. 2(b)].…”

“…Because Np is conserved, the expansion (13) can be regarded as a difFerential equation for w(t). We can readily find the first integral of Eq.…”

“…In all the cases, instead of the quadratic equation (17), we should consider the more general analytical model defined by Eqs. (13) or (15) Fig. 2(a)].…”

Spatial optical solitons in highly nonlocal media

“…With a few * Corresponding author: alessandro.alberucci@gmail.com exceptions in reorientational liquid crystals [38][39][40], however, longitudinal nonlocal effects are usually neglected, that is, the Laplacian operator lacks the partial derivative along the propagation direction. This is appropriate only for shapepreserving beams and/or in the absence of power dissipation; even without losses, in fact, the family of self-confined waves includes breathing solitons subject to bounded periodic oscillations of their width and peak intensity [16,17,[41][42][43]. In such cases, the refractive index gradient along the direction of propagation affects the self-trapped wave packet.…”