Abstract
Numerical experiments and a theoretical study are made for the diatomic Toda lattice equation to show the existence of stationary nonlinear gap modes. The characteristic properties of the nonlinear localized mode obtained numerically and analytically using the rotating-wave approximation are: (1) It arises from the soft anharmonicity of an effective potential for the Toda lattice. (2) Its central position is located at the site of a lighter atom. (3) Its eigenfrequency is splitted from the bottom of the optic frequency band. (4) The gap mode profile is composed of two parts, a localized s-like vibrational mode and a lattice distortion. (5) For not too large anharmonicity, there exists a simple relationship between a shift function and an envelope function representing the lattice distortion and the vibrational amplitude, respectively.
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