Continuous approximation of breathers in one- and two-dimensional DNLS lattices

In this paper we construct and approximate breathers in the DNLS model starting from the continuous limit: such periodic solutions are obtained as perturbations of the ground state of the NLS model in H(1)(R(n)), with n = 1, 2. In both the dimensions we recover the Sievers-Takeno and the Page (P) modes; furthermore, in R(2) also the two hybrid (H) modes are constructed. The proof is based on the interpolation of the lattice using the finite element method (FEM).