Stationary and moving intrinsic localized modes in one-dimensional monatomic lattices with cubic and quartic anharmonicity

By locally distorting a perfect one-dimensional lattice that contains a cubic and quartic nonlinearity in the nearest-neighbor potential, we demonstrate that self-localized vibrational modes are stable even for large cubic anharmonicities. Simulations are used to test the eigenvectors and eigenfrequencies of both stationary and moving localized modes. The frequency of the localized vibration decreases with increasing cubic anharmonicity until it approaches the maximum plane-wave frequency, where the mode becomes unstable. As the cubic anharmonicity increases, the eigenvector also becomes more localized until it resembles a triatomic molecule, beyond which the mode again becomes unstable. This study examines intrinsic localized modes over the complete range of possible anharmonicity and amplitude values.