A sequence of nonlinear, time-dependent second order differential equations describing the motion of an infinite one-dimensional periodic lattice 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 several examples this approach provides an accurate and efficient computational tool. An existence criterion to be satisfied by the potential is worked out for the considered vibrational modes.

• Received 21 February 1997

DOI:https://doi.org/10.1103/PhysRevE.57.1134