Topological discrete kinks

A spatially discrete version of the general kinkbearing nonlinear KleinGordon model in di mensions is constructed which preserves the topological lower bound on kink energy It is proved that provided the lattice spacing h is suciently small there exist static kink solutions attaining this lower bound centred anywhere relative to the spatial lattice Hence there is no PeierlsNabarro barrier impeding the propagation of kinks in this discrete system An upper bound on h is derived and given a physical interpretation in terms of the radiation of the system The construction which works most naturally when the nonlinear KleinGordon model has a squared polynomial interaction potential is applied to a recently proposed continuum model of polymer twistons Numerical simulations are presented which demonstrate that kink pinning is eliminated and radiative kink deceleration greatly reduced in comparison with the conventional discrete system So even on a very coarse lattice kinks behave much as they do in the contin uum It is argued therefore that the construction provides a natural means of numerically simulating kink dynamics in nonlinear KleinGordon models of this type The construction is compared with the inverse method of Flach Zolotaryuk and Kladko Using the latter method alternative spatial discretizations of the twiston and sineGordon models are obtained which are also free of the PeierlsNabarro barrie