Solitary plane waves in an isotropic hexagonal lattice

Abstract

Solitary plane-wave solutions in a two-dimensional hexagonal lattice which can propagate in different directions on the plane are found by using the pseudospectral method. The main point of our studies is that the lattice model is isotropic and we show that the sound velocity is the same for different directions of wave propagation. The pseudospectral method allows us to obtain solitary wave solutions with very narrow profile, the thickness of which may contain a few atoms or even less than one lattice spacing (i.e., essentially discrete solutions). Since these nonlinear waves are quite narrow, details of lattice microstructure appear to be important for their motion. Particularly, the regime of their propagation qualitatively depends on whether or not the direction of their motion occurs along the lattice bonds. Two types of solitary plane waves are found and studied. The stability of these solitary waves is investigated numerically by their interactions with vacancies and lattice edges. Propagation of solitary plane waves through finite lattice domains with isotopic disorder is extensively studied. Comparison of these results with the soliton propagation in one-dimensional lattices with mass impurities is presented.