Suppression of transverse instabilities of dark solitons and their dispersive shock waves

Abstract

We investigate the impact of nonlocality, owing to diffusive behavior, on transverse instabilities of a dark\ud stripe propagating in a defocusing cubic medium. The nonlocal response turns out to have a strongly stabilizing\ud effect both in the case of a single soliton input and in the regime where dispersive shock waves develop\ud multisoliton regime. Such conclusions are supported by the linear stability analysis and numerical simulation\ud of the propagation

Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier

“…In that case, the suppression of the DSS instability is provided by the nonlocal character of the respective mean-field model (see also Ref. [37] for similar results in the context of optics). A more complex dark-soliton configuration, which is not subject to the MI, was reported in Refs.…”

Observation of surface dispersive shock waves in a self-defocusing medium

“…In nonlinear optics, DSWs were initially studied in optical fibers in the temporal domain [13,14]. Recently, DSWs with a laser beam as an initial input have been the subject of intense study in many optical systems, including photorefractive media [15][16][17], thermal media [18][19][20][21][22][23][24], nematic liquid crystals [25], nonlinear arrays [26], quadratic media [27], disordered media [28], and nonlinear junctions [29]. Here, diffractions result in spatial dispersion that regularizes the shock front through the onset of fast oscillations in an expanding region after the wave-breaking points.…”

Ring dark and antidark solitons in nonlocal media

“…This occurs, e.g., in media featuring strong thermal nonlinearity [12] or in nematic liquid crystals [13], where the nonlinear contribution to the refractive index depends on the intensity distribution in the transverse plane. It has been shown that dark solitons in one-dimensional (1D) settings exist in media with a defocusing nonlocal nonlinearity [14][15][16][17][18][19] while, in the case of stripes, transverse MI may be suppressed due to the nonlocality [20]. The smoothing effect of the nonlocal response was shown to occur even in the case of shock wave formation [20][21][22][23], or give rise to stable 2D solitons [24].…”

“…It has been shown that dark solitons in one-dimensional (1D) settings exist in media with a defocusing nonlocal nonlinearity [14][15][16][17][18][19] while, in the case of stripes, transverse MI may be suppressed due to the nonlocality [20]. The smoothing effect of the nonlocal response was shown to occur even in the case of shock wave formation [20][21][22][23], or give rise to stable 2D solitons [24]. Here we should note that, generally, pertinent nonlocal models do not possess soliton solutions in explicit form (other than the weakly nonlinear limit [25]).…”