Existence and stability of breathers in lattices of weakly coupled two-dimensional near-integrable Hamiltonian oscillators

A method of proving the existence of breathers in lattices of two-dimensional weakly coupled Hamiltonian oscillators is presented. This method has the advantage that provides a first approximation of the initial conditions of the breather solution together with its linear stability. Since the proof relies on the use of action-angle variables, we also present a method to perform the calculations without knowledge of the specific transformation. We illustrate the results in a lattice of quartic oscillators and in another one that consists of coupled 2D Morse oscillators. Finally, we examine the possibility of extending these results in lattices of more than two degrees of freedom per lattice site.