It has been shown recently that a moving discrete breathers localized in one close-packed atomic row can be excited in a two-dimensional monoatomic crystal with Morse interaction. In this work, a motionless discrete breathers having the threefold symmetry axis has been excited in the same crystal. The initial conditions for the excitation of such discrete breathers are set by the superposition of a bell-shaped function on a planar nonlinear phonon mode with the wave vector lying at the edge of the Brillouin zone. In addition, the displacement of the centers of atomic oscillations from the center of the discrete breathers owing to the asymmetry of the Morse potential is taken into account. The results obtained make it possible to approach the search for highly symmetric discrete breathers in three-dimensional crystals.

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Based on the results of molecular dynamics simulations the characteristics of discrete breathers (DB) in two-dimensional (2D) and three-dimensional (3D) crystals with Morse long-range interatomic interactions are compared. It is demonstrated that DB in 3D crystal have higher frequencies and higher degree of localization than in 2D crystal.

The work presents a comparison of characteristics of discrete breathers (DB) excited in the close-packed two-dimensional Morse crystal with two different values of the potential stiffness parameter. The dependence of DB frequency on its amplitude for both crystals is calculated.