Moving Self-Localized Modes for the Displacement Field in a One-Dimensional Lattice System with Quartic Anharmonicity

Abstract

A numerical experiment and an analytical calculation are made to study self-localized modes for the displacement field of a pure one-dimensional lattice with hard quartic anharmonicity. Approximate analytical solutions are obtained for moving localized modes with eigenfrequencies above the top of the harmonic frequency band. The envelope of the displacement field itself is of the form of the conventional sech function, depending on the wave vector of carrier waves. By using approximate analytical solutions as input, numerical experiments are made to explore the space-time evolution of the localized modes by taking the localized mode height and the wave vector of carrier waves as parameters. It is shown that the moving localized modes obtained here are identifiable as lattice solitons under favorable conditions.