Date: Monday, September 13, 2021
Location: ZOOM ID: 922 9373 3366 Virtual (3:30 PM to 4:30 PM)
Title: Longtime asymptotics of KdV dispersive shock wave via RiemannHilbert problems
Abstract: In this talk we will summarize a recent paper on the KdV equation with steplike initial data. The focus lies on the DeiftZhou nonlinear steepest descent analysis in the transition region, where solutions converge to a modulated elliptic (ItsMatveev) solution. We state the corresponding RiemannHilbert problem, as well as the global parametrix (model) problem. Surprisingly, the global parametrix problem has in general no matrix valued solution. We thus have to rely on a vectorvalued model solution and compare it directly to the exact solution. For this we rely on the work of Zhou on Fredholm index theory for singular integral operators.
A recording of the talk can be found here.
Files:
Speaker: Mateusz Piorkowski
Institution: MSRI
Event Organizer: Ahmad Barhoumi barhoumi@umich.edu
