Small amplitude breathers in 1D and 2D Klein-Gordon lattices

We construct small amplitude breathers in one-dimensional (1D) and two-dimensional (2D) Klein-Gordon (KG) infinite lattices. We also show that the breathers are well-approximated by the ground state of the nonlinear Schrdinger equation. The result is obtained by exploiting the relation between the KG lattice and the discrete nonlinear Schrdinger model. The proof is based on a Lyapunov-Schmidt decomposition and continuum approximation techniques introduced in [Bambusi and Penati, Continuous approximation of ground states in DNLS lattices, Nonlinearity 23 (2010), pp. 143-157], actually using its main result as an important lemma.