Super Bloch oscillations in the Peyrard-Bishop-Holstein model

► We study the Peyrard-Bishop-Holstein model under superimposed DC and AC fields. ► The detuning between the driven and the Bloch frequency sets the polaron dynamics. ► The carrier displays super Bloch oscillations for the non-resonant cases. ► The Morse potential sets the lattice motion which is decoupled of the carrier one. ► The nonlinear coupling leads to a distortion of the wave packet at long times.