Chirped soliton solutions of the cubic-quintic Swift-Hohenberg equation with space-dependent coefficients

The optical pulses generation in mode-locked lasers are described, in the case of complicated spectral filtering, by the cubic-quintic complex Swift-Hohenberg equation (CQSHE). Using the ansatz method, we studied the existence of the bright and dark chirped soliton solutions of the space-dependent coefficients CQSHE. The physical parameters of the chirped soliton solutions have been obtained as functions of the variable coefficients of the model equation. The parametric conditions for the existence of the chirped soliton solutions are presented. By the numerical evolution of the bright and dark solitons, we studied the influence of high order effects, dispersion and nonlinearity's, on the propagation of the soliton solutions.