Jack Arbunich : Rigorous derivation of Nonlinear Dirac equations describing wave dynamics in Honeycomb lattices

Posted by Mimi Dai , part of the Analysis and Applied Mathematics Seminar.

At

March 13, 2017, 4 p.m.

In

SEO 636

Abstract

We present recent work (jointly with C. Sparber) on the weakly nonlinear wave dynamics occurring in cubic nonlinear Schrödinger equations with a periodic honeycomb lattice potential. Using a semiclassical scaling, we rigorously derive an effective macroscopic model of nonlinear Dirac type. To this end we employ a multi-scale asymptotic expansion together with rigorous error estimates in certain scaled Sobolev spaces. If time permits, we shall also discuss the case of a non-local Hartree nonlinearity.