Nonlinear wave interactions in 1D crystals with complex lattice

Plane oscillations of a chain of "dumb-bell"-shaped particles are considere d. This system models dynamics of the quasi-one-dimensional crystals consis ting of anisotropic molecules of stretched shape. The governing equations d escribing the anharmonic interaction between elastic and orientational wave s in a lattice are derived for a cubic potential of the interparticle inter action in the discrete and continuous models. It is shown that, in the low- frequency approximation, the governing equations are analogous to the equat ions of the second-order gradient theory of elasticity that are used for de scription of nonlinear phenomena in layered crystals and structural transfo rmations in alloys. Investigations of three-wave interactions point to poss ible excitation of orientational waves in organic crystals due to their non linear coupling with acoustic waves. (C) 1999 Elsevier Science B.V. All rig hts reserved.