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Nonlinear localized excitations in one-dimensional diatomic lattices withcubic and quartic nonlinearity are considered analytically by aquasi-discreteness approach. The criteria for the occurence of asymmetric gapsolitons (with vibrating frequency lying in the gap of phonon bands) andsmall-amplitude, asymmetric intrinsic localized modes (with the vibratingfrequency being above all the phonon bands) are obtained explicitly based onthe modulational instabilities of corresponding linear lattice plane waves. Theexpressions of particle displacement for all these nonlinear localizedexcitations are also given. The result is applied to standard two-bodypotentials of the Toda, Born-Mayer-Coulomb, Lennard-Jones, and Morse type. Thecomparison with previous numerical study of the anharmonic gap modes indiatomic lattices for the standard two-body potentials is made and goodagreement is found.Comment: 24 pages in Revtex, 2 PS figure

Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity