Dissipative solitons under the action of the third-order dispersion

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 dinstict 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 approximate to -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). [S1063-651X(99)07709-0].