LOCALIZED VIBRATIONS AND STANDING WAVES IN ANHARMONIC LATTICES

A sequence of nonlinear, time-dependent second order differential equa tions describing the motion of an infinite one-dimensional periodic la ttice of arbitrary anharmonicity is considered. It is converted to an equivalent time-independent integrodifferential system, solved for all localized vibrational modes and standing waves. As illustrated by sev eral examples this approach provides an accurate and efficient computa tional tool. An existence criterion to be satisfied by the potential i s worked out for the considered vibrational modes.