Anisotropic characters in two-dimensional hexagonal crystal

The anisotropic characters of two-dimensional hexagonal crystal are investigated in this paper. The dispersion relation has been studied numerically. It is shown that the dispersion relation strongly dependents on the directions of wave propagation. Generally, the direction of waves has the inclination angle ϕ with respect to particle displacement. There are compressional waves ϕ = 0 or transverse waves ϕ = π/2 for long wavelength. However, for short wavelength compressional and transverse waves exists only for some special directions. For most cases, neither compressional nor transverse waves exists. The nonlinear waves in this crystal have also been studied. The characters of solitons, such as amplitude and width, have been investigated.