Influence of external phase and gain-loss modulation on bound solitons in laser systems

We study the dynamics of bound solitons of the complex cubic-quintic Ginzburg- Landau equation under the influence of external modulation. We consider periods of modulation being either smaller or larger than the soliton separation and the amplitude of modulation being either real or imaginary. For each case, we observe bifurcation and hysteresis phenomena in the parameters of the pair when changing the amplitude of modulation. Namely, soliton separation and phase difference between the solitons may take two or more values for the same modulation amplitude. In the case of gain-loss modulation, two solitons may split and be positioned in the two equilibrium states of the periodic potential. The complicated dynamics of this process is illustrated with numerical examples.