Stationary breather model in a two-dimensional hexagonal spring-mass lattice

Abstract

In the present paper, the form of stationary breather modes in a two-dimensional (2D) FPU-KG spring mass lattice that exhibits square and hexagonal symmetry is studied. Inspired by the work of Marin et al. (1998) [6], we develop a solution with the breathers' energy primarily focused in 3 major chains. To express the approximate shape of breather in the small amplitude limit, an asymptotic approximation to the breathers is built by applying the method of multiple scales. The dispersion relation formed exhibits intriguing forms, i.e., -3 types of solution at certain wavenumbers. Numerical simulations of the lattices are conducted to verify the shape of breathers, and it is noticed that the breather persists for long times at a relatively larger natural frequency Ω0. When Ω0≫O(1), the breather may remain a relatively long-lived mode as we observe that the energy is slowly transferred from the centre of the lattice to the rest of sites with the wave propagating though the lattice.