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 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