  We show strong effects of a weak and smooth, on the magnetic length,
superlattice potential upon edge magnetoplasmons (EMPs) at the armchair edge,
with a smooth steplike electrostatic lateral confining potential, of a wide
graphene channel in the $\nu=2$ quantum Hall effect regime. The superlattice
potential leads to essential enlargement of a number of EMPs, descend from two
fundamental EMPs in the absence of superlattice. For the wave vector $k_{x}$
within the first Brillouin zone, the EMPs show as the regions of acoustical or
quasi-acoustical dispersion, with a finite value of group velocity, so the
regions with frequency gaps, where a group velocity is nullified at some
$k_{x}$. We obtain that for $k_{x} \to 0$ only for two EMPs the frequency tends
to zero as for other EMPs it obtains finite values. Strong dependence of
dispersion relations of the EMPs from the period of the superlattice $a_{0}$
and the distance $d$ from a metallic gate is shown; in particular, for typical
size of a gap, for characteristic value of the frequency and $k_{x}$ at which
the group velocity is reduced to zero. At the frequency that corresponds to
zero group velocity of pertinent fundamental EMP branch the response of the
system should present a strong resonance.
