title: Dissipative solitons under the action of the third-order dispersion.
abstract: We study the evolution of a solitary pulse in the cubic complex Ginzburg-Landau equation, including the third-order dispersion (TOD) as a small perturbation. We develop analytical approximations, which yield a TOD-induced velocity c of the pulse as a function of the ratio D of the second-order dispersion and filtering coefficients. The analytical predictions show agreement with the direct numerical simulations for two distinct intervals of D. A new feature of the pulse motion, which is a precursor of the transition to blowup, is presented: The pulse suddenly acquires a large acceleration in the reverse direction at D>D(cr) approximately -1.5 and without the reversal at D<D(cr). It is also demonstrated that the laminar-propagation distance L (before the onset of the ultimate turbulent stage) becomes maximum deep inside the normal-dispersion region, while TOD significantly increases L in the anomalous-dispersion region, where, otherwise, it is quite small. The model has a straightforward physical realization in terms of nonlinear optical fibers with losses and bandwidth-limited amplification (gain and filtering).
authors.affiliation: Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel. malomed@eng.tau.ac.il
authors.forename: B A
authors.initials: BA
authors.lastname: Malomed
authors.forename: D J
authors.initials: DJ
authors.lastname: Frantzeskakis
authors.forename: H E
authors.initials: HE
authors.lastname: Nistazakis
authors.forename: A
authors.initials: A
authors.lastname: Tsigopoulos
authors.forename: K
authors.initials: K
authors.lastname: Hizanidis