Nonlinear gap modes in a 1D alternating bond monatomic lattice with anharmonicity

We analytically study the nonlinear localized gap modes in a one-dimensiona l atomic chain with uniform atomic mass but two periodically alternating fo rce constants between the nearest neighbors by means of a quasi-continuum a pproximation. This model simulates a row of atoms in the (111) direction of a diamond-structure type of crystals or molecular crystals with alternatin g double and single bonds. For this lattice system, rye find that the harmo nic plus quartic anharmonic terms of inter-site potential produce a new typ e of nonlinear localized gap modes with a slightly asymmetry distribution o f atomic displacements. These localized gap modes are somewhat different fr om widely studied localized gap modes with a symmetry atomic displacement d istribution in diatomic ion lattices.