Orateur
Joanne Dong
(University of Michigan)
Description
We discuss some progress in formulating the Riemann-Hilbert problem associated with the Defocusing Nonlinear Schrodinger (dNLS) equation with nonzero boundary conditions. This project builds on the work of Jin, Levermore, and McLaughlin, and aims to describe the solution to dNLS after the shock forms and the Madelung description of the problem breaks down. By strengthening the limit in recovering the solution to dNLS from the Riemann-Hilbert problem, we hope to contribute another verification of the Dubrovin-Grava-Klein-Moro universality conjecture.