Discreteness effects on non-topological kink soliton dynamics in nonlinear lattices

Abstract

We show that discreteness effects which are known to exist for topological solitons exist also for non-topological kink solitons in nonlinear lattices. Extending the technique previously proposed for topological kinks we exhibit three cases where the properties of narrow kinks in nonlinear lattices are qualitatively different. Supersonic solitons in a monoatomic chain can propagate at constant speed without losing energy due to discreteness. Subsonic kinks in a monoatomic chain permanently radiate small amplitude oscillations. In a diatomic chain both supersonic and subsonic kinks lose energy due to discreteness. The characteristics of the small amplitude oscillations radiated by the kinks, when they exist, are well determined by our theoretical approach. Additional weak nonlinear effects are also described and discussed.