Desynchronization of temporal solitons in Kerr cavities with pulsed injection

A numerical and analytical study was conducted to investigate the bifurcation mechanisms that cause desynchronization between the soliton repetition frequency and the frequency of external pulsed injection in a Kerr cavity described by the Lugiato-Lefever equation. The results suggest that desynchronization typically occurs through an Andronov-Hopf bifurcation. Additionally, a simple and intuitive criterion for this bifurcation to occur is proposed.