  Ranges of existence and stability of dark cavity-soliton stationary states in
a Fabry-Perot resonator with a Kerr nonlinear medium and normal dispersion are
determined. The Fabry-Perot configuration introduces nonlocal coupling that
shifts the cavity detuning by the round trip average power of the intracavity
field. When compared with ring resonators described by the Lugiato-Lefever
equation, nonlocal coupling leads to strongly detuned dark cavity solitons that
exist over a wide range of detunings. This shift is a consequence of the
counterpropagation of intracavity fields inherent to Fabry-Perot resonators. At
difference with ring resonators, the existence and stability of dark soliton
solutions are dependent on the size and number of solitons in the cavity. We
investigate the effect of nonlocal coupling of Fabry-Perot resonators on
multiple dark solitons and demonstrate long range interactions and
synchronization of temporal oscillations.
