Soliton dynamics of nonlinear diatomic lattices

Abstract

We study analytically and numerically a nonlinear diatomic chain with cubic and/or quartic interaction potential between first- and second-nearest neighbors. In the continuum approximation using a decoupling ansatz for the motion of the two different sublattices we obtain supersonic or subsonic acoustic kink (pulse) solitons, long-wavelength acoustic oscillating solutions of breather type, and purely optical-envelope-type excitations. We then introduce an analytical technique which enables us to calculate oscillating soliton solutions of the symmetric or asymmetric envelope or hole (dark) type, modulating a quasiharmonic carrier the wave vector of which is not limited to long wavelength. The characteristic energies of all these kinds of excitations are given as a function of the main parameter. Numerical simulations on their propagation and interactions show these excitations to be long-lived quasisolitons.