Guided waves in a multi-layered optical structure

Motivated by the study of the propagation of electromagnetic waves through a multi-layered optical medium, we prove the existence of two different kinds of homoclinic solutions to the origin in a Schrödinger equation with a nonlinear term. We use a Krasnoselskii fixed point theorem together with a compactness criterion due to Zima. The main results are illustrated with concrete examples of practical interest such as self-focusing nonlinearities of Kerr and non-Kerr type.