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.

Amplitude response, Melnikov's criteria, and chaos occurrence in a Duffing's system subjected to an external periodic excitation with a variable shape.

The present study considers the nonlinear dynamics of a Duffing oscillator under a symmetric potential subjected to a pulse-type excitation with a deformable shape. Our attention is focused on the effects of the external excitation shape parameter r and its period. The frequency response of the system is derived by using a semi-analytical approach. Interestingly, the frequency-response curve displays a large number of resonance peaks and anti-resonance peaks as well. Surprisingly, a resonance phenomenon termed here as shape-induced-resonance is noticed as it occurs solely due to the change in the shape parameter of the external periodic force. The system exhibits amplitude jumps and hysteresis depending on r. The critical driving magnitude for the chaos occurrence is investigated through Melnikov's method. Numerical analysis based on bifurcation diagrams and Lyapunov exponent is used to show how chaos occurs in the system. It is shown that the threshold amplitude of the excitation to observe chaotic dynamics decreases/increases for small/large values of r. In general, the theoretical estimates match with numerical simulations and electronic simulations as well.

Higher-order dispersion and nonlinear effects of optical fibers under septic self-steepening and self-frequency shift.

We investigate the modulational instability (MI) of a continuous wave (cw) under the combined effects of higher-order dispersions, self steepening and self-frequency shift, cubic, quintic, and septic nonlinearities. Using Maxwell's theory, an extended nonlinear Schrödinger equation is derived. The linear stability analysis of the cw solution is employed to extract an expression for the MI gain, and we point out its sensitivity to both higher-order dispersions and nonlinear terms. In particular, we insist on the balance between the sixth-order dispersion and nonlinearity, septic self-steepening, and the septic self-frequency shift terms. Additionally, the linear stability analysis of cw is confronted with the stability conditions for solitons. Different combinations of the dispersion parameters are proposed that support the stability of solitons and the occurrence of MI. This is confronted with full numerical simulations where the input cw gives rise to a broad range of behaviors, mainly related to nonlinear patterns formation. Interestingly, under the activation of MI, a suitable balance between the sixth-order dispersion and the septic self-frequency shift term is found to highly influence the propagation direction of the optical wave patterns.

Modulational instability of a trapped Bose-Einstein condensate with two- and three-body interactions.

We investigate analytically and numerically the modulational instability of a Bose-Einstein condensate with both two- and three-body interatomic interactions and trapped in an external parabolic potential. Analytical investigations performed lead us to establish an explicit time-dependent criterion for the modulational instability of the condensate. The effects of the potential as well as of the quintic nonlinear interaction are studied. Direct numerical simulations of the Gross-Pitaevskii equation with two- and three-body interactions describing the dynamics of the condensate agree with the analytical predictions.

Modulated waves and pattern formation in coupled discrete nonlinear LC transmission lines.

The conditions for the propagation of modulated waves on a system of two coupled discrete nonlinear LC transmission lines with negative nonlinear resistance are examined, each line of the network containing a finite number of cells. Our theoretical analysis shows that the telegrapher equations of the electrical transmission line can be reduced to a set of two coupled discrete complex Ginzburg-Landau equations. Using the standard linear stability analysis, we derive the expression for the growth rate of instability as a function of the wave numbers and system parameters, then obtain regions of modulational instability. Using numerical simulations, we examine the long-time dynamics of modulated waves in the line. This leads to the generation of nonlinear modulated waves which have the shape of a soliton for the fast and low modes. The effects of dissipative elements on the propagation are also shown. The analytical results are corroborated by numerical simulations.

Modulational instability in a purely nonlinear coupled complex Ginzburg-Landau equations through a nonlinear discrete transmission line.

We study wave propagation in a nonlinear transmission line with dissipative elements. We show analytically that the telegraphers' equations of the electrical transmission line can be modeled by a pair of continuous coupled complex Ginzburg-Landau equations, coupled by purely nonlinear terms. Based on this system, we investigated both analytically and numerically the modulational instability (MI). We produce characteristics of the MI in the form of typical dependence of the instability growth rate on the wavenumbers and system parameters. Generic outcomes of the nonlinear development of the MI are investigated by dint of direct simulations of the underlying equations. We find that the initial modulated plane wave disintegrates into waves train. An apparently turbulent state takes place in the system during the propagation.

Comment on "Defocusing complex short-pulse equation and its multi-dark-soliton solution".

In their recent paper, Feng et al. [Phys. Rev. E 93, 052227 (2016)PREHBM2470-004510.1103/PhysRevE.93.052227] proposed a complex short-pulse equation of both focusing and defocusing types. They studied in detail the defocusing case and derived its multi-dark-soliton solutions. Nonetheless, from a physical viewpoint in order to better and deeply understand their genuine implications, we find it useful to provide a real and proper background for the derivation of the previous evolution system while showing that the expression of the nonlinear electric polarization the above authors used in their scheme is not suitable for getting the defocusing complex short-pulse equation.

Thermal nucleation of kink-antikink pairs in the presence of impurities: the case of a Remoissenet-Peyrard substrate potential.

Thermal nucleation of kink-antikink pairs in a nonlinear Klein-Gordon (NKG) model with a Remoissenet-Peyrard (RP) substrate potential in the presence of impurities and coupled to an applied field is analyzed in the limits of moderate temperature and strong damping. Using the Kolmogorov method, the average velocity of particles of the lattice is calculated and its dependence on the intensity of impurities is discussed in connection with the deformability parameter or the shape of the RP substrate potential. Numerical values are carried out by making use of parameters of the hydrogen atom adsorbed in the tungsten and ruthenium substrates. We show that, for large values of the applied field, the presence of impurities in the system makes the nucleation process of kink-antikink pairs more favorable in the high-temperature regime while they contribute to make it less favorable in the low-temperature regime.

Analytical calculation of the Peierls-Nabarro barriers for the Remoissenet-Peyrard substrate potential.

We derive analytically the pinning potential and the pinning barrier of kinks due to discreteness of lattices for the Remoissenet-Peyrard substrate potential by means of the residue method. The theoretical analysis in the low discreteness effect regime is compared in detail with numerical results of Peyrard and Remoissenet [Phys. Rev. B 26, 2886 (1982)], yielding a very satisfactory agreement.

Ultrashort optical waveguide excitations in uniaxial silica fibers: elastic collision scenarios.

In this work, we investigate the dynamics of an uniaxial silica fiber under the viewpoint of propagation of ultimately ultrashort optical waveguide channels. As a result, we unveil the existence of three typical kinds of ultrabroadband excitations whose profiles strongly depend upon their angular momenta. Looking forward to surveying their scattering features, we unearth some underlying head-on scenarios of elastic collisions. Accordingly, we address some useful and straightforward applications in nonlinear optics through secured data transmission systems, as well as laser physics and soliton theory with optical soliton dynamics.

Soliton interactions between multivalued localized waveguide channels within ferrites.

In this paper, we investigate both analytically and numerically the localized multivalued waveguide channels-the loop solitons-dynamics within a ferrite slab. In the starting point of the work, we solve in detail the initial value problem of the system while unveiling the existence of multivalued waveguide channels solutions. Paying particular interest to the nonlinear scattering among these excitations, we study extensively the different kinds of interacting features between these localized waves alongside the depiction of their energy densities. As a result, we find that the interactions can be attractive or repulsive depending strongly on the ratio of the amplitudes of the interacting structures. In the wake of these results, we address some physical implications, accordingly.

Dynamics of kink-dark solitons in Bose-Einstein condensates with both two- and three-body interactions.

The matter-wave solutions of Bose-Einstein condensates with three-body interaction are examined through the one-dimensional Gross-Pitaevskii equation. By using a modified lens-type transformation and a further extension of the tanh-function method we obtain the exact analytical solutions which describe the propagation of kink-shaped solitons, anti-kink-shaped solitons, and other families of solitary waves. We realize that the shape of a kink solitary wave depends on both the scattering length and the parameter of atomic exchange with the substrate. The stability of the solitary waves is examined using analytical and numerical methods. Our results can also be applied to nonlinear optics in the presence of cubic-quintic media.

Wave train generation of solitons in systems with higher-order nonlinearities.

Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain. Experimental values are used for the numerical simulations and the input plane wave leads to the development of pulse trains, depending upon the sign of the septic nonlinearity.

Generation of pulse trains in nonlinear optical fibers through the generalized complex Ginzburg-Landau equation.

We consider a higher-order complex Ginzburg-Landau equation, with the fourth-order dispersion and cubic-quintic nonlinear terms, which can describe the propagation of an ultrashort subpicosecond or femtosecond optical pulse in an optical fiber system. We investigate the modulational instability (MI) of continuous wave solution of this equation. Several types of modulational instability gains are shown to exist in both the anomalous and normal dispersion regimes. We find that depending on the sign of the fourth-order dispersion coefficient, the MI appears for normal and anomalous dispersion regime. Simulations of the full system demonstrate that the development of the MI leads to establishment of a regular or chaotic array of pulses, a chain of well-separated peaks with continuously growing or decaying amplitudes depending on the sign of the loss/gain coefficient and higher-order dispersions terms. Comparison of the calculations with reported numerical results shows a satisfactory agreement.