Deniz Bilman : On long time asymptotics of integrable systems and their perturbations, solitons, and the inverse scattering transform.

Posted by Jonah Gaster , part of the Graduate Student Colloquium.

At

March 18, 2013, 4:15 p.m.

In

SEO 636

Abstract

I will briefly introduce the Fermi-Pasta-Ulam (FPU) lattices, and talk on how a humble experiment started a new era in nonlinear evolution equations. Then I will consider the doubly infinite Toda lattice, introduce the notion of complete integrability and soliton solutions along with some other interesting properties of this system. Within this framework, I will briefly cover Lax formalism and the inverse scattering transform which is a method for solving integrable systems. Finally, I will talk on the "soliton resolution conjecture" and discuss the long time asymptotics problem for the lattices obtained by perturbations of the integrable Toda potential. I will mention a few results along with some interesting obstacles towards the solution to this problem. The talk is intended to be self-contained and accessible to graduate students from different fields. There will be three short movies and two pictures.