Dynamics of Pereira-Stenflo Solitons in the Presence of Third-Order Dispersion
Abstract
Evolution of a solitary pulse in the cubic complex Ginzburg-Landau (CGL) equation, 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 direct 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≅-3/2, and a less steep jump in the opposite direction at -30<D<-20, each jump changing the sign of the velocity. The simulations also demonstrate that there is a maximum of the laminar propagation distance (before the onset of the ultimate turbulent stage) attained at D≅-18. The action of the sliding-frequency filtering on the soliton dynamics is also investigated numerically, and it is found that it slightly increases the laminar propagation distance.
- Publication:
-
Physica Scripta Volume T
- Pub Date:
- 1999
- DOI:
- 10.1238/Physica.Topical.082a00036
- Bibcode:
- 1999PhST...82...36M
- Keywords:
-
- 52.35.Sb;
- 52.35.Mw;
- 52.35.Ra