Self-Localized Modes in a Pure One-Dimensional Lattice with Cubic and Quartic Lattice Anharmonicity

A pure one-dimensional lattice with cubic and quartic anharmonicity is studied to show the existence of two types of self-localized modes, one is stationary and the other mobile. For the former, the lattice Green's function method is employed to formulate the frequency and a profile function of a fundamental mode and those of higher harmonics. An s -like symmetry mode and a p -like one are shown to be physically interesting. In the one-localized-mode problem, approximate analytical expressions for these quantities are obtained in the extreme localization. The cubic anharmonicity is shown to introduce a tiny kink-like distortion attached to the localized mode. For a propagating localized mode, numerical and approximate analytical calculations are done to show the existence of a well-defined p -like mode.