Existence and Stability of Two-Dimensional Compact-Like Discrete Breathers in Discrete Two-Dimensional Monatomic Square Lattices

Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generalized discrete two-dimensional monatomic model. It is proven that the two-dimensional compact-like discrete breathers exist not only in two-dimensional soft ψ⁴ potentials but also in hard two-dimensional ψ⁴ potentials and pure two-dimensional K₄ lattices. The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional ψ⁴ potential are determined by coupling parameter K₄, while those in pure two-dimensional K₄ lattices have no coupling with parameter K₄. The stabilities of
the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K₄ and the boundary condition of lattices.