Influence of the intrapulse Raman scattering on the localized pulsating solutions of generalized complex-quintic Ginzburg-Landau equation

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

“…Now in system (3) the corresponding term 8 15 c g 2 r 2 , which, of course, is transformed into the first one assuming that rðxÞ ¼ 1=gðxÞ as is usually accepted in the soliton perturbation theory. The derived system (3) on the one hand generalizes the earlier results of [32] and [19,20] and on the other hand presents a general approach avoiding the restrictions of the previous approaches [29,30,24,31] for the analysis of the influence of the IRS, SS and TOD on the solutions of CCQGLE. The price to be paid, however, is the complexity of the derived system.…”

“…Using the ansatz of the traveling wave and fixing some relations between the material parameters, the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave has been derived [29,30]. Next, the Melnikov method has been applied to this equation and the existence of a limit cycle has been shown.…”

“…One of our aims is to propose a general approach for the study of the influence of the IRS, SS and TOD on all of the solutions of CCQGLE avoiding the restrictions of previous approaches [29,30,24,31]. As it is well known the method of moments [32] could be useful for the analysis of stationary solutions, pulsating solutions and moving fronts [19,20].…”

“…An approach has been presented for the identification of periodic attractors of the generalized CCQGLE with IRS [29,30]. Using the ansatz of the traveling wave and fixing some relations between the material parameters, the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave has been derived [29,30].…”

“…Next, the Melnikov method has been applied to this equation and the existence of a limit cycle has been shown. The stability of this limit cycle has been proved in [29,30]. A perturbation theory for the description of the influence of the nonlinear refraction index, IRS and TOD on the stable stationary solutions below the PAHB identified in [24] has been proposed in [31].…”