Sensitive behaviors of intrinsic localized modes in the presence of impurity and random inhomogeneity

Abstract

Behaviors of the intrinsic localized modes (ILMs) in inhomogeneous nonlinear lattice with quartic anharmonicity have been investigated numerically. Numerically generated ILM is introduced into lattices with a single mass impurity or random mass inhomogeneity and its evolutions are pursued. In case of a single impurity, a variety of processes, such as, reflection, mode change, trapping, and segmentation are observed according to the change in impurity mass. In case of random inhomogeneity, meandering of the ILM and eventual trapping are observed when the variance signifying randomness is relatively large, while continuous gradual damping due to multiple scattering are observed for cases with relatively small variances. It is found that even a small inhomogeneity of lattice scale affects significantly the behavior of the ILMs in contrast to the case of soliton. It is pointed out that the interaction process of ILM with an impurity differs from that with random inhomogeneity and the former process has an analogy with the energy level considerations for atomic spectra.