Travelling kinks in discrete ϕ4 models

In recent years, three exceptional discretizations of the ϕ4 theory have been discovered (by Speight and Ward, Bender and Tovbis, and Kevrekidis) which support translationally invariant kinks, i.e. families of stationary kinks centred at arbitrary points between the lattice sites. It has been suggested that the translationally invariant stationary kinks may persist as sliding kinks, i.e. discrete kinks travelling at nonzero velocities without …