  In the present paper we study phase waves of self-sustained oscillators with
a nearest neighbor dispersive coupling on an infinite lattice. To analyze the
underlying dynamics we approximate the lattice with a quasi-continuum, QC. The
resulting partial differential model is then further reduced to the Gardner
equation which predicts many properties of the underlying solitary structures.
Using an iterative procedure on the original lattice equations we determine the
shapes of solitary waves, kinks, and the flat-like solitons, that we refer to
as flatons. Direct numerical experiments reveal that the interaction of
solitons and flatons on the lattice is notably clean. All in all we find that
both the QC and the Gardner equation predict remarkably well the discrete
patterns and their dynamics.
