Kink-soliton explosions in generalized Klein–Gordon equations

We investigate the dynamics of kink-solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We present different mechanisms for kink-soliton explosion and show that, in some cases while some analytically obtained conditions are satisfied, the kink-soliton breaks up becoming a permanent, extremely complex, spatiotemporal dynamics. We perform computer simulations in order to visualize and corroborate our analytical findings. The mechanisms presented for kink-soliton breakup can explain some of the phenomena that recently have been reported to occur in excitable media. Finally, we will present a way to control soliton breakup, using appropriate external perturbations.