We study the soliton time shift in the presence of linear and nonlinear gain, saturation of the nonlinear refractive index, spectral filtering, third-order of dispersion and self-steepening effect. The applied model generalizes the complex cubicquintic Ginzburg-Landau equation (CCQGLE) with the basic higher-order effects in fibers: the intrapulse Raman scattering (IRS), third-order of dispersion (TOD) and self-steepening effect. Soliton perturbation theory (SPT) is derived with which the influence of the saturation of the nonlinear refraction index, self-steepening and TOD on the appearance of the Poincare-Andronov-Hopf bifurcation is analyzed. It has been shown that TOD and self-steepening effect can lead to reduction in the time shift of the pulse. This prediction has been verified by numerical solution of generalized CCQGLE.
In this paper we present numerical investigation of the influence of intrapulse Raman scattering (IRS) on the stable stationary pulses. Our basic equation, namely cubic-quintic Ginzburg-Landau equation describes the propagation of ultra-short optical pulses under the effect of IRS in the presence of linear and nonlinear gain as well as spectral filtering. Our aim is to examine numerically the influence of IRS, on the stable stationary pulses in the presence of constant linear and nonlinear gain as well as spectral filtering. Numerical solution of our basic equation is performed by means of the “fourth-order Runge-Kutta method in the interaction picture method” method. We found that the small change of the value of the parameter which describes IRS leads to qualitatively different behavior of the evolution of pulse amplitudes. In order to study the observed strong dependence on the IRS, the perturbation method of conserved quantities of the nonlinear Schrodinger equation is applied. The numerical analysis of the derived nonlinear system of ordinary differential equations has shown that our numerical findings are related to the existence of the Poincare-Andronov-Hopf bifurcation.
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