  Abstract Interaction equations governing slow time evolution of the
coordinates and phases of two interacting temporal cavity solitons in a delay
differential equation model of a nonlinear mirror mode-locked laser are derived
and analyzed. It is shown that non-local pulse interaction due to gain
depletion and recovery can lead either to a development of harmonic
mode-locking regime, or to a formation of closely packed incoherent soliton
bound state with weakly oscillating intersoliton time separation. Local
interaction via electric field tails can result in an anti-phase or in-phase
stationary and breathing harmonic mode-locking regimes.
