Travelling fronts in a piecewise-linear bistable system

The piecewise-linear model of a continuous bistable system is considered. Two different classes of the fronts, namely the bistable fronts (BFs), which perform the transition from the least stable to the most stable state of the system, and the pulled fronts, which perform the transition between the unstable and stable states, are examined within the considered model. The exact front solutions that describe the free, undisturbed fronts are derived for the most general case of the piecewise-linear approximation used. The limiting cases of the motionless and the fast propagating BFs are analysed. The deterministic front `ratchet' effect, a new possibility of the ac driven direct motion of the BFs, is discussed.