  The temporal Talbot effect refers to the periodic self-imaging of pulse
trains in optical fibers. The connection between the linear and nonlinear
temporal Talbot effect is still not fully understood. To address this
challenge, we use Soliton Radiation Beat Analysis and numerically investigate
the evolution of a phase-modulated continuous-wave laser input in a passive
single-mode fiber. We identify three input-power-dependent regimes and their
Talbot carpets: the quasi-linear regime for low input powers, the intermediate
one, and separated Talbot solitons for higher powers. We show that the
intermediate regime hosts soliton crystals rather than rogue waves, as reported
in the literature. The Talbot-solitons beating can be used for pulse
repetition-rate multiplication in the nonlinear regime. We also show two types
of solitons involved: some encoded in the whole frequency comb and the
individual solitons carried only by particular comb lines.
