Kink compactons in models with parametrized periodic double-well and asymmetric substrate potentials

We derive kink solutions with compact support (kink compactons) in a nonlinear Klein–Gordon system with anharmonic coupling. The model is characterized by the double-well Remoissenet–Peyrard (RP) substrate potential VRP (θ, r) whose shape can be moved as a function of the parameter r in the range 0 r<1. The phase trajectories, as well as an analytical analysis, provide information on a disintegration of kink compactons upon reaching some critical values of the lattice parameters. Exact analytic expressions for the dependence of this threshold value on the nonlinear parameter, on the velocity of the kink compactons and on the shape parameter are derived. The dependence of the four classes of kink compacton solutions, on the shape parameter r is obtained, and the total energies of each class of kink compactons are exactly calculated.