Surface breathers in discrete magnetic metamaterials

Abstract

We analyze the properties of discrete breathers excited near the edge of a one-dimensional metamaterial created by a truncated array of nonlinear split-ring resonators. We study a crossover between nonlinear surface states and discrete breathers by analyzing the modes centered at finite distances from the array edge and demonstrate the existence of a class of nonlinear localized surface states, the so-called nonlinear Tamm states or surface breathers, which exhibit features that have no counterparts either in the continuous systems or in linear arrays.