  Dissipative quartic solitons have gained interest in the field of mode-locked
lasers for their energy-width scaling which allows the generation of ultrashort
pulses with high energies. Pursuing the characterization of such pulses, here
we found soliton solutions of a distributed model for mode-locked lasers in the
presence of either positive or negative fourth order dispersion (4OD). We
studied the impact the laser parameters may have on the profiles, range of
existence and energy-width relation of the output pulses. The most energetic
and narrowest solutions occur for negative 4OD, with the energy having an
inverse cubic dependence with the width in most cases. Our simulations showed
that the spectral filtering has the biggest contribution in the generation of
short (widhts as low as 39 fs) and very energetic (392 nJ) optical pulses.
