  We analyze the impact of pump depletion in the generation of cavity solitons
in a singly-resonant parametrical oscillator that includes a $\chi^{(3)}$
nonlinear section. We find an analytical expression that provides the soliton
existence region using variational methods, study the efficiency of energy
conversion, and compare it to a driven Kerr resonator modeled by the
Lugiato-Lefever equation. At high walk-off, solitons in singly-resonant optical
parametric oscillators are more efficient than those formed in a Kerr resonator
driven through a linear coupler.
