Solitary-wave propagation in the three-dimensional lattice

Abstract

The properties of solitary waves in a three-dimensional monatomic face-centered-cubic lattice are studied. The atoms of the lattice are assumed to interact via a Morse-type interatomic potential. For the discrete lattice, the equations of motion for the atoms are solved numerically using a computer-molecular-dynamic technique and, from their solution, the stability of the waves investigated. It is pointed out that the solitary waves are fairly stable to longitudinal planar oscillations, somewhat less stable to mutual collisions, and still less stable to transverse planar oscillations. It is also observed that under some conditions coupled longitudinal and transverse solitary waves can propagate in phase with the same propagation velocity in the lattice. The equations of motion are then derived in the long-wavelength continuum limit and studied in some detail. A comparison of their solutions is made with the results for the discrete-lattice model and it is shown that the continuum equations are capable of predicting many of the same effects.