Phonon scattering by localized equilibria of nonlinear nearest-neighbor chains

We study scattering of phonons by localized equilibria, for example, localized defects on nonlinear chains. We show that perfect transmission occurs at $k=0\mathrm{}$ at the threshold for creation of localized modes and there exists a characteristic transition involving perfect transmission of long-wavelength phonons near the threshold. The theory is illustrated for the stationary case of a discrete kink on a translationally invariant Hamiltonian nearest neighbor chain, which is then generalized to any symmetric localized defects. The implications for discrete breathers are also discussed.