Special ACM/CMS Seminar

In this talk, I present a discrete nonlinear Schrödinger equation (DNLS) that models the propagation of laser beams in waveguide arrays built on nematic liquid crystal substrates. The interaction between electromagnetic waves and the liquid crystal director field gives rise to a nonlocal nonlinearity for the amplitude equation of a modulated plane wave. We focus on the existence of breather-type solutions to the DNLS and analytical approximations to these breathers. I will present different types of solutions (peaks and shelf-type solutions) in two cases: with local and nonlocal interaction, in the limit when the linear coupling vanishes. Extensions of these solutions based on the implicit function theorem and analytical approximations based on a variational approach will also be discussed.