Exact discrete compactlike traveling kinks and pulses in phi(4) nonlinear lattices

We show that by properly choosing the analytical form of a solitary wave solution of discrete phi(4) models we can calculate the parameters of the potential which allow the propagation of compact (kink and pulses) solutions. Our numerical simulations show that narrow kinks and pulses with finite extent can propagate freely, and that discrete breathers with finite but long lifetime, can emerge from their collisions. Moreover, our numerical simulations reveal that the propagation of two successive pulses at a relative distance of two lattice spacings propagate freely, i.e., without interaction.