Anharmonic localized surface vibrations in a scalar model

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Abstract
Anharmonic excitations have been found and investigated that are localized at the surface of one-, two-, and three-dimensional lattices having simple cubic structures. A scalar model has been used with a single scalar degree of freedom per lattice point and short-range interactions. The nonlinear modes involve only a small number of particles or are extended along the surface. The stability of the nonlinear excitations has been analyzed and the nonlinear dynamics induced by an instability has been monitored by molecular dynamics.