Jack Arbunich : Modeling Nonlinear Wave Dynamics in Honeycomb Structures

Posted by Trevor Leslie , part of the Graduate Analysis Seminar.

At

March 8, 2017, 4 p.m.

In

SEO 512

Abstract

We will consider the nonlinear Schrödinger equation in two spatial dimensions subject to a periodic honeycomb lattice potential. Using a multiscale expansion together with rigorous error estimates, we will derive an effective model of nonlinear Dirac type. The latter describes the propagation of slowly modulated, weakly nonlinear waves spectrally localized near a Dirac point. The aim of the talk will be to introduce the theory of periodic Schrödinger operators and to familiarize the audience with the formal technique of multiscale expansion.