Kink dynamics in a lattice model with long-range interactions

This paper proposes a one-dimensional lattice model with long-range interac tions which, in the continuum, keeps its nonlocal behaviour. In fact, the l ong-time evolution of the localized waves is governed by an asymptotic equa tion of the Benjamin-One type and allows the explicit construction of movin g kinks on the lattice. The long-range particle interaction coefficients on the lattice are determined by the Benjamin-One equation.