Influence of higher-order effects on pulsating solutions, stationary solutions and moving fronts in the presence of linear and nonlinear gain/loss and spectral filtering

• Published in: Optical fiber technology Vol. 24; pp. 15 - 23
• Main Authors: Uzunov, Ivan M., Arabadzhiev, Todor N., Georgiev, Zhivko D.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.08.2015
• Subjects: Cubic–quintic complex Ginzburg–Landau equation; Fiber lasers; Higher-order effects; Nonlinear fiber optics; Poincare–Andronov–Hopf bifurcation; Soliton transmission systems; Soliton transmission systems; Higher-order effects; Poincare–Andronov–Hopf bifurcation; Nonlinear fiber optics; Cubic–quintic complex Ginzburg–Landau equation; Fiber lasers
• ISSN: 1068-5200; 1095-9912
• DOI: 10.1016/j.yofte.2015.04.003

•We have studied the influence of the higher- order effects IRS, TOD and SS on the pulsating solutions, moving fronts and stationary solutions of CCQGLE which have been found in [6,19,20] as well as the pulsating and stationary solutions of [24].•Using the method of moments [32] we have reduced the infinite-dimensional dynamical dissipative system which represents the generalized CCQGLE to a finite-dimensional dynamical system. It has been found that PAHB due to IRS [24] also exists in the dynamical system (3). The derived dynamical system (3) could serve as a basis for the further bifurcation analysis.•New localized fluctuating and stationary solutions have been obtained for fairly large values of parameters of IRS and TOD, respectively.•The transformation of the stable stationary solution of [24] under the influence of SS into pulsating solution has been numerically observed. This fact could be interpreted as the existence of PAHB. We have studied the impact of the higher-order effects: intrapulse Raman scattering (IRS), third-order of dispersion (TOD) and self-steepening (SS) on pulsating solutions, moving fronts and stationary solutions of the complex cubic–quintic Ginzburg–Landau equation (CCQGLE) found in Tsoy and Akhmediev (2005) as well as on the solutions presented in Uzunov et al. (2014). The applied basic equation generalizes the CCQGLE with the IRS, TOD and SS effects. A finite-dimensional dynamical system has been derived using the method of moments. Applying the derived dynamical system alongside with the numerical solution of the generalized CCQGLE performed by means of the fourth-order Runge–Kutta interaction picture method we have found that the influence of IRS and SS is stronger than the impact of TOD for the solutions of Tsoy and Akhmediev (2005). Perturbed pulsating solutions, moving fronts and stationary solutions in the presence of IRS, SS and TOD have been numerically observed. They exist up to some critical values of the parameters of perturbations. For the values of parameters larger than the critical ones the pulsating solutions are transformed into stable stationary solutions or unstable solutions. New localized fluctuating and stationary solutions have been obtained for fairly large values of parameters of IRS and TOD, respectively. The transformation of the stable stationary solution of Uzunov et al. (2014) under the influence of SS into pulsating solution has been numerically observed.