Solitons and periodic wave solutions for complex Ginzburg-Landau equation modelling fiber lasers and nonequilibrium phenomena

Abstract

New types of soliton and periodic waves are identified for a nonlinear dissipative medium where the pulse propagation is governed by the cubic complex Ginzburg-Landau equation. We find that the dynamical equation for the pulse amplitude supports two distinct types of kink and antikink solitons with different functional forms. It is found that the obtained kink and antikink soliton waveforms occur under the same fixed inverse velocity. The results also indicate that the periodic waves can propagate with variety of wave forms such as sn, cn, dn and their rational forms as well. It is also shown that in the long-wave limit, the derived periodic waves degenerate into different bright and dark soliton pulses. The stability analysis based on the theory of dispersive waves in nonlinear optics is developed. It is shown that some elliptic and soliton solutions are quasi-stable in the context of passive mode locking lasers described by complex Ginzburg-Landau equation.