Abstract
The equations of motion for longitudinal and transverse waves in a non-linear, dispersive three-dimensional elastic continuum and the conditions under which these waves retain their initial longitudinal or transverse character are obtained. The equations of motion have the one-dimensional continuum form and hence the standing wave results described previously may be applied to the three-dimensional continuum. The example of the rare-gas solids is discussed. The analysis is based on a 6-12 interatomic potential and a FCC lattice. It is found that for the three symmetry directions 100, 110, 111 only the three longitudinal waves and one of the 110 transverse waves can retain their initial character and the standing-wave effects would be masked by acoustic damping above 1K in argon.