Gap solitons in diatomic lattices

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Abstract
We consider a nonlinear diatomic lattice of the Klein-Gordon type composed of particles with two different masses. The linear spectrum of this model exhibits a gap, which is proportional to the mass difference in addition to the natural gap stipulated by a nonlinear substrate potential. We analyze the coupled nonlinear excitations of such a diatomic chain which have a similar origin as the well-known gap solitons appearing in nonlinear (e.g., optical) systems with a spatial periodicity. We also describe dark-profile localized structures with a frequency lying below the gap. In the limit when the gap disappears, i.e., for the case of a monoatomic chain, the gap solitons do not exist but instead there exist localized structures of a distinct type created by the nonlinearity-induced symmetry breaking between two equivalent eigenmodes of the lattice, the so-called self-supporting gap solitons.