Oscillations of a highly discrete breather with a critical regime

We analyze carefully the essential features of the dynamics of a stationary discrete breather in the ultimate degree of energy localization in a nonlinear Klein-Gordon lattice with an on-site double-well potential. We demonstrate the existence of three different regimes of oscillatory motion in the breather dynamics, which are closely related to the motion of the central particle in an effective potential having two nondegenerate wells. In given parameter regions, we observe an untrapped regime, in which the central particle executes large-amplitude oscillations from one to the other side of the potential barrier. In other parameter regions, we find the trapped regime, in which the central particle oscillates in one of the two wells of the effective potential. Between these two regimes we find a critical regime in which the central particle undergoes several temporary trappings within an untrapped regime. Importantly, our study reveals that in the presence of purely anharmonic coupling forces, the breather compactifies, i.e., the energy becomes abruptly localized within the breather.