  We consider an optical resonator containing a photonic crystal fiber and
driven coherently by an injected beam. This device is described by a
generalized Lugiato-Lefever equation with fourth order dispersion. We use an
asymptotic approach to derive interaction equations governing the slow time
evolution of the coordinates of two interacting dissipative solitons. We show
that Cherenkov radiation induced by positive fourth-order dispersion leads to a
strong increase of the interaction force between the solitons. As a
consequence, large number of equidistant soliton bound states in the phase
space of the interaction equations can be stabilized. We show that the presence
of even small spectral filtering not only dampens the Cherenkov radiation at
the soliton tails and reduces the interaction strength, but can also affect the
the bound state stability.
