A discrete $\phi^4$ system without a Peierls - Nabarro barrier

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Abstract
A discrete system is proposed which preserves the topological lower bound on the kink energy. Existence of static kink solutions saturating this lower bound and occupying any position relative to the lattice is proved. Consequently, kinks of the model experience no Peierls - Nabarro barrier, and can move freely through the lattice without being pinned. Numerical simulations reveal that kink dynamics in this system is significantly less dissipative than that of the conventional discrete system, so that even on extremely coarse lattices the kink behaves much like its continuum counterpart. It is argued, therefore, that this is a natural discretization for the purpose of numerically studying soliton dynamics in the continuum model.
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