Nonlocal dark solitons under competing cubic–quintic nonlinearities

Abstract

We investigate properties of dark solitons under competing nonlocal cubic-local quintic nonlinearities. Analytical results, based on a variational approach and confirmed by direct numerical simulations, reveal the existence of a unique dark soliton solutions with their width being independent of the degree of nonlocality, due to the competing cubic-quintic nonlinearities.

Interactions of nonlocal dark solitons under competing cubic–quintic nonlinearities

“…The local quintic contribution to nonlocal cubic nonlinearity has profound effects on the bright and dark solitons in the regime of weak nonlocality [31]. Recently, we have revealed that the local quintic contribution to nonlocal cubic nonlinearity can support unique dark soliton solutions with their width being independent of the degree of nonlocality in the limit of strong nonlocality [32].…”

“…For simplicity, and without loss of generality, we consider, here, the rectangular profile for the nonlocal response function, Rx [16,25,32,33]:…”

“…It can be shown that the Lagrangian density corresponding to the nonlocal NLS, Eq. (1), is of the following form [32]:…”

Stability of vortex solitons under competing local and nonlocal cubic nonlinearities

“…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. The competing effect of local and nonlocal nonlinearities can support multipole solitons [43], promote shape transformations of gap solitons in optical lattice [53], and stabilize accessible light bullets [54,55] and dark solitons [56,57]. Recently, the bifurcated vortex solitons were studied in media with competing nonlocal cubic and local quintic nonlinearities, which shows that the vortex solitons located in the lower branch always split into multipole scalar solitons in the limit of weak nonlocality and propagate stably only when the degree of nonlocality is sufficiently strong.…”

Stabilization of vortex solitons by combining competing cubic-quintic nonlinearities with a finite degree of nonlocality

“…By combining competing and nonlocal nonlinearities, higher-order vortex solitons are shown to be stable [28]. Moreover, solitons with even and odd parities [29], gap solitons [30], accessible light bullets [31], and dark solitons [32][33][34] are studied in nematic liquid crystals [35] or Bose-Einstein condensates [36] in which thermal and orientational effects or simultaneous contact and long-ranged dipolar interactions act as competing nonlocal nonlinearities.…”