A Propagating Self-Localized Mode in a One-Dimensional Lattice with Quartic Anharmonicity

Abstract

A pure one-dimensional lattice with quartic anharmonicity and nearest-neighbor interactions is shown to exhibit a fairly well-defined propagating self-localized mode above the harmonic frequency band. This is a propagating-mode version of a stationary, immobile p-like self-localized mode having the displacement pattern (…, 0, 0, −1⁄2, 1/2, 0, 0, …) in the extreme localization limit. An approximate analytical expression for localized-mode envelope functions is obtained in a form similar to that of the Ablowitz-Ladik lattice solitons. Nonlinear eigenvalue equations are studied by using the method of lattice Green’s functions, by which an approximate analytical expression for the dispersion relation of the localized mode is also obtained.