Bound states of plain and composite pulses: Multi-soliton solutions

We investigate numerically the formation and stability characteristics of bound states in the complex Ginzburg-Landau equation, considering both plain and composite pulses. Our numerical results show the existence of stable bound states of two plain or composite pulses when the phase difference between them is ±π/2. Two-composite pulses bound states have zero velocity, which is in contrast with the behavior of the bound states formed by plain pulses. The possibility of constructing multi-soliton solutions is demonstrated. In particular, we show the possibility of constructing stable bound states of multiple plain pulses with zero velocity by choosing appropriately the phase profile of the whole solution.