  A soliton explosion is an instability whereby a dissipative soliton undergoes
a sudden structural collapse, but remarkably returns back to its original shape
after a short transient. We recently reported the first experimental
observation of this effect in a fiber laser (A. F. J. Runge et al., Optica 2,
36 (2015)). Here, we expand on our initial work, presenting a more detailed
experimental and numerical study of the characteristics and dynamics of soliton
explosions in passively mode-locked fiber lasers. Specifically, we explore
different cavity configurations and gain levels, observing and characterizing
explosion events using spectral and temporal real-time single-shot techniques.
Our results highlight that the explosion characteristics observed in
experiments depend critically on the position in the cavity where the output
coupler is located. Furthermore, we find that the frequency at which explosions
occur can be controlled by adjusting the pump power. We also identify a new
kind of ``partial'' explosion, where strong spectral interference fringes
appear on the pulse spectra, but a full collapse is avoided. Finally, we
perform numerical simulations based on a realistic iterative cavity map, and
obtain results that are in good agreement with experimental measurements.
Careful analysis of the simulation results provide strong credence to the
interpretation that soliton explosions can be linked to a multi-pulsing
instability.
