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
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.
higher-order effects nonlinear fiber optics fiber lasers soliton transmission systems cubicquintic complex ginzburglandau equation poincareandronovhopf bifurcation