Discrete breathers in a two-dimensional spring-mass lattice

Abstract

We consider a two-dimensional spring-mass lattice with square symmetry in which each particle experiences a nonlinear onsite potential and nonlinear nearest-neighbour interactions. At equilibrium, the particles are equally spaced in both the horizontal and vertical directions and all springs are unextended. Motivated by the work of Marin et al (1998 Phys. Lett. A 248 225–9, 2001 Phys. Lett. A 281 21–5), we seek a solution in which most of the breather's energy is focused along three chains. We construct an asymptotic approximation to the breather using the method of multiple scales to describe the coherent oscillations in the three main chains that constitute the discrete breather. We reduce the equation of motion to a nonlinear Schrödinger equation for the leading-order term and find a family of solutions, which encompasses both stationary and moving bright soliton solutions. We use numerical simulations of the lattice to verify the shape and velocity of breathers and find that while stationary breathers are found to persist for long times, moving breathers decay by radiating energy in the direction perpendicular to their motion.