Low-Frequency and High-Frequency Moving Anharmonic Localized Modes in a One-Dimensional Lattice with Quartic Anharmonicity

The existence of two branches of moving anharmonic localized modes is shown for a one-dimensional (1D) lattice with hard quartic anharmonicity. By the use of a pair of exactly solvable model nonlinear lattice equations as a reference system, approximate analytical expressions for envelope functions, the eigenfrequencies and the velocities of low- and high-frequency modes are obtained for each of envelope-kinklike modes and envelope-solitonlike modes. The approximate analytical results are tested by numerical experiments to show that these two branches of the modes are robust against generation at initial stages of ripples, eventually preserving their own profiles as time evolves.