  Propagation of transition fronts in models of coupled oscillators with
non-degenerate on-site potential is usually considered in terms of travelling
waves. We show that the system dynamics can be reformulated as an implicit map
structure, and the travelling waves correspond to stable fixed points.
Therefore, the loss of stability of such waves should follow well-known generic
bifurcation scenarios. Then, one can expect a plethora of qualitatively
different propagating-front solutions - multistable, multi-periodic,
quasiperiodic and chaotic.
