Multisolitons-like patterns in a one-dimensional MARCKS protein cyclic model.

In this paper, we study the nonlinear dynamics of the MARCKS protein between cytosol and cytoplasmic membrane through the modulational instability phenomenon. The reaction-diffusion generic model used here is firstly transformed into a cubic complex Ginzburg-Landau equation. Then, modulational instability (MI) is carried out in order to derive the MI criteria.

Robustness of rogue waves: the route to improve the ultrafast propagation of pulses in wave guide structures.

In this work, an adaptive control of instability is used to improve the ultrafast propagation of pulses in wave guide structures. One focuses on robust wave profiles with ideal shape and amplitude that can be useful for the ultrafast propagation without severe perturbations. The few perturbations observed are managed to catch up the stability of pulses and pick up the ultrafast propagation.

Pure quartic modulational instability in weakly nonlocal birefringent fibers.

The modulational instability (MI) phenomenon is theoretically investigated in birefringent optical media with pure quartic dispersion and weak Kerr nonlocal nonlinearity. We find from the MI gain that instability regions are more expanded due to nonlocality, which is confirmed via direct numerical simulations showing the emergence of Akhmediev breathers (ABs) in the total energy context. In addition, the balanced competition between nonlocality and other nonlinear and dispersive effects exclusively gives the possibility of generating long-lived structures which deepens our understanding of soliton dynamics in pure-quartic dispersive optical systems and opens new investigation routes in fields related to nonlinear optics and lasers.

Interplay between spin-orbit couplings and residual interatomic interactions in the modulational instability of two-component Bose-Einstein condensates.

The nonlinear dynamics induced by the modulation instability (MI) of a binary mixture in an atomic Bose-Einstein condensate (BEC) is investigated theoretically under the joint effects of higher-order residual nonlinearities and helicoidal spin-orbit (SO) coupling in a regime of unbalanced chemical potential. The analysis relies on a system of modified coupled Gross-Pitaevskii equations on which the linear stability analysis of plane-wave solutions is performed, from which an expression of the MI gain is obtained. A parametric analysis of regions of instability is carried out, where effects originating from the higher-order interactions and the helicoidal spin-orbit coupling are confronted under different combinations of the signs of the intra- and intercomponent interaction strengths.

Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity.

The modulational instability (MI) phenomenon is addressed in a nonlocal medium under controllable saturation. The linear stability analysis of a plane-wave solution is used to derive an expression for the growth rate of MI that is exploited to parametrically discuss the possibility for the plane wave to disintegrate into nonlinear localized light patterns. The influence of the nonlocal parameter, the saturation coefficient, and the saturation index are mainly explored in the context of a Gaussian nonlocal response.