P-Like Stationary Self-Localized Modes in Pure One-Dimensional Lattice with Quartic Lattice Anharmonicity

Abstract

A pure one-dimensional anharmonic lattice with quartic lattice anharmonicity and nearest neighbour interactions is shown to exhibit a p -like stationary self-localized mode. This is an intrinsic nonlinear mode with eigenfrequency higher than that of an s -like mode to which attention has been focussed so far. Tking the displacement differences between nearest neighbour pairs of atoms as relevant field variables leads to a much simpler formulation as compared to the case of the s -like mode. By introducing lattice Green's functions and using a rotating-wave approximation (RWA), analytical expressions are obtained for the eigenfrequency and eigenfuntions for a p -like mode appearing far above the harmonic frequency band. The RWA itself is also examined to show that it is a good and working approximation procedure for anharmonic-localized-mode problems.