  Oscillons are time-dependent, localized in space, extremely long-lived states
in nonlinear scalar-field models, while kinks are topological solitons in one
spatial dimension. In the present work, we show new classes of oscillons and
oscillating kinks in a system of two nonlinearly coupled scalar fields in $1 +
1$ spatiotemporal dimensions. The solutions contain a control parameter, the
variation of which produces oscillons and kinks with a flat-top shape. The
model finds applications to condensed matter, cosmology, and high-energy
physics.
