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Analytical theory of large size intrinsic localized modes (ILMs) inanharmonic two-atomic chain is presented. It is shown that ILMs withfrequencies close to the borders of phonon gap are govern by quarticanharmonicity while the effect of cubic anharmonicity is essentially reduced.This reduction effect is a consequence of small amplitude of vibrations ofevery second atom. As a result, an ILM cannot split down from the opticalphonon band, in contradiction with the commonly accepted point of view. But itcan spit up from the top of the acoustic phonon band making possible theexistence of the ILM with the frequencies above the top of this band. It ispredicted that analogous reduction of cubic anharmonicity should existgenerally for even ILMs with the middle atom being at rest; it may allow theexistence of ILMs with the frequencies above the top of the phonon spectrum indifferent lattices with realistic atomic pair-potentials.

Intrinsic localized modes in two atomic chain; reduction of cubic anharmonicity for gap modes