Dynamics of Pereira-Stenflo solitons in the presence of third-order dispersion

Evolution of a solitary pulse in the cubic complex Ginzburg-Landau (CGL) eq uation, including third-order dispersion (TOD) as a small perturbation, is studied in detail. Starting from the exact Pereira-Stenflo soliton solution , we develop analytical approximations which yield an effective velocity c of the pulse induced by TOD. The analytical predictions are compared to dir ect numerical simulations, showing acceptable agreement at small values of the TOD parameter, provided that the second-order dispersion coefficient D takes values D > -3/2 or D < -30 (very different analytical approximations are used in these two cases). Between these regions, the numerically found dependence c(D) shows a very steep jump at D congruent to -3/2, and a less steep jump in the opposite direction at -30 < D < -20, each jump changing t he sign of the velocity. The simulations also demonstrate that there is a m aximum of the laminar propagation distance (before the onset of the ultimat e turbulent stage) attained at D congruent to -18. The action of the slidin g-frequency filtering on the soliton dynamics is also investigated numerica lly, and it is found that it slightly increases the laminar propagation dis tance.