STATIONARY ANHARMONIC GAP MODES IN A ONE-DIMENSIONAL DIATOMIC LATTICE WITH QUARTIC ANHARMONICITY

Stationary anharmonic localized modes with eigenfrequencies appearing in the gap between the optic and acoustic frequency bands are studied for a one-dimensional diatomic lattice with hard or soft quartic anharmonicity. A systematic analytical scheme using the lattice Green's function method combined with the rotating-wave approximation and its improved version is developed on the one hand, and extensive numerical experiments have been made on the other. The eigenfrequencies and profile functions of anharmonic gap modes are obtained both analytically and numerically. Good quantitative agreement between the theoretical result and the experimental ones is obtained for both of the gap modes due to the hard and soft quartic anharmonicity. It is shown that the spatial localization of the latter is much more pronounced than that of the former.