Dark solitons in nonlocal media with competing nonlinearities

Abstract

We investigate analytically and numerically the propagation properties of dark solitons in nonlocal media with competing nonlinearities. We obtain analytical relations for soliton parameters for an arbitrary degree of nonlocality. In particular, we show that the velocity of dark solitons can be affected by the degree of nonlocality of competing nonlinearities. The analytical results are confirmed by direct numerical simulations of the full model describing propagation of dark solitons in nonlocal media with competing nonlinearities.

The interaction of dark solitons with competing nonlocal cubic nonlinearities

“…The positive and negative signs of the index α 2 represent the competing self-focusing and self-defocusing nonlinearities, respectively. It has also been shown that the stationary dark soliton solution always exists if α 1 + α 2 < 0 [68,72].…”

“…We should emphasize that (16) describes exactly the dark solitons in media with competing nonlocal cubic nonlinearities obtained previously [72].…”

“…Although (12) is only a phenomenological model, it also can describe the general properties of the nonlocal media very well. In particular, with such a model of nonlocal response function, the solutions of dark solitons can be obtained analytically in the whole range of nonlocality [39,52,70,72]. Substituting (4) and (12) into the Lagrangian density (11) and integrating over the whole spatial coordinate x, we can obtain the averaged Lagrangian of the following form…”

“…For the sake of simplicity and analytical tractability and without loss of generality, however, we consider here the rectangular profile for the nonlocal response function [39,52,70,72]:…”

Stability of vortex solitons under competing local and nonlocal cubic nonlinearities

“…The competing nonlinearities of media induced by different physical processes contribute to the overall nonlinear response, for example, simultaneous local and long range interaction in Bose-Einstein condensation [33], and thermal and orientational nonlinearities in nematic liquid crystal [31,34]. The competing nonlocal nonlinearities have profound effect on the formation of novel solitons' states [35][36][37][38][39][40] and the interactions of bright and dark solitons [41,42]. Besides the model with synthetic double nonlocal nonlinearities [31,[37][38][39][40][41][42], the competing effect between local and nonlocal nonlinearities has also drawn considerable attention [43][44][45][46][47][48][49][50][51][52] in both optics and Bose-Einstein condensates.…”