Higher-order correction terms to the nonlinear amplification or absorption, the nonlinear refractive index, and the intrapulse Raman scattering.

In this paper we have investigated through the numerical solution of the basic equation as well as through the dynamic model the influence of higher-order correction terms to the nonlinear amplification (absorption) and to the nonlinear refractive index on the self-frequency shift of Raman dissipative solitons. We have found a nonlinear dependence of the self-frequency shift of Raman dissipative solitons on the parameter describing intrapulse Raman scattering in the presence of the saturation of the nonlinear gain. With the increase of the absolute value of the saturation of the nonlinear gain, the maximum absolute value of the frequency shift decreases and its position moves to larger values of the parameter describing intrapulse Raman scattering. The increase in the value of the nonlinear gain leads to an increase in the maximum absolute value of the frequency shift, without changing its position. We have also observed the nonlinear dependence of the absolute value of the frequency shift on the parameter describing intrapulse Raman scattering in the presence of higher-order correction term to the nonlinear refractive index. The discovered nonlinear dependence of the self-frequency shift on the value of the saturation of the nonlinear gain as well as on the higher-order correction term to the nonlinear refractive index can be used for the better understanding and control of the spectral characteristics of Raman dissipative solitons. The dynamic model correctly describes all the features of the observed phenomena.

Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects.

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.

Influence of intrapulse Raman scattering on stationary pulses in the presence of linear and nonlinear gain as well as spectral filtering.

We examine numerically the influence of intrapulse Raman scattering (IRS) on the stable stationary pulses in the presence of constant linear and nonlinear gain as well as spectral filtering. Numerical results show that the small change of the value of the parameter describing IRS leads to qualitatively different behavior of the evolution of pulse amplitudes. We prove that the strong dependence of the pulse dynamics on the parameter describing IRS is related to the existence of the Poincaré-Andronov-Hopf bifurcation and the appearance of the unstable limit cycle.

Suppression of the soliton self-frequency shift and compression in the presence of bandwidth-limited amplification.

We study numerically the suppression of the soliton self-frequency shift as well as the compression in the presence of bandwidth-limited optical amplification (BLA). Our results confirm the existence of equilibrium points (stable focuses) for the soliton amplitude and speed identified by the soliton perturbation theory. Analyzing the equilibrium amplitudes as a function of physical parameters, maximum compression factor in the amplification of short pulses is revealed. The results of linear stability analysis allow estimation of the necessary distance for the appearance of equilibrium states from different initial conditions. It has been shown that the shape of the perturbed stationary solution in the presence of intrapulse Raman scattering and BLA can be described by the earlier derived analytic expressions.