J. Szeftel et P. Laurent, LOCALIZED VIBRATIONS AND STANDING WAVES IN ANHARMONIC LATTICES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 57(1), 1998, pp. 1134-1138
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.