STATIONARY VIBRATIONAL-MODES OF A CHAIN OF PARTICLES INTERACTING VIA AN EVEN ORDER POTENTIAL

For a monatomic one-dimensional chain of particles interacting via a nearest neighbor potential of any even order, it is shown that there are stationary vibrational modes (SVMs) periodic in time with stable spatial configuration. The SVM is the exact solution of the classical equations of motion of the particles of the chain interacting via the potentials considered. A recurrence relation determining the spatial configuration and an equation determining the time dependence of these modes have been obtained. It is shown that the intrinsic localized vibrations (ILVs) which have been recently studied (by Page) for this system of particles are the exact solutions of the classical equations of motion. New types of ILVs involving more particles than recently predicted (by Page) have been found. © 1990.