On the continuum limit for a model of binary waveguide arrays

Abstract

In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existence of localized standing waves. This work rigorously justifies formal arguments and numerical simulations present in the Physics literature.

arXiv commentThe proof of Lemma 11 has been corrected, and the statement of Theorems 2 and 5 modified. Final version to appear on NoDEA