Analysis and Applied Mathematics Seminar
Rigorous derivation of Nonlinear Dirac equations describing wave dynamics in Honeycomb lattices
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.
Monday March 13, 2017 at 4:00 PM in SEO 636