Damping and pumping of localized intrinsic modes in nonlinear dynamical lattices

It has been recently demonstrated that dynamical models of nonlinear lattices admit approximate solutions in the form of self-supported intrinsic modes (IM's). In this work, the intensity of the emission of radiation ("phonons") from the one-dimensional IM is calculated in an analytical approximation for the case of a moderately strong anharmonicity. Contrary to the emission in nonintegrable continuum models, which may be summarized as fusion of several vibrons into a phonon, the emission in the lattice may be described in terms of fission of a vibron into several phonons: as the IM's internal frequency lies above the phonon band of the lattice, the radiative decay of the IM in the discrete system can be only subharmonic. It is demonstrated that the corresponding lifetime of the IM may be very large. Then, the threshold (minimum) value of the amplitude of an external ac field, necessary to support the IM in a lattice with dissipative losses, is found for the limiting cases of the weak and strong anharmonicity.