Self-frequency shift effect on dissipative soliton bound states

We investigate numerically the impact of the self-frequency shift effect on isolated and bound states of some soliton-like (plain and composite) solutions of the complex Ginzburg–Landau equation. In the absence of the self-frequency shift effect, stable bound states are found for a phase difference of ±π/2 between the constituent plain, respectively, composite, pulses. In the presence of such effect, the corresponding stationary points remain symmetrically located in the interaction plane, but the line joining them is rotated in the counterclockwise direction. Moreover, we verify that one of these points remains a stable stationary point, whereas the other one turns out to be unstable. It is shown that the bound states propagate with the same velocity as the single pulses.