Seminar Event Detail

Integrable Systems and Random Matrix Theory

Date:  Monday, September 13, 2021
Location:  ZOOM ID: 922 9373 3366 Virtual (3:30 PM to 4:30 PM)

Title:  Long-time asymptotics of KdV dispersive shock wave via Riemann-Hilbert problems

Abstract:   In this talk we will summarize a recent paper on the KdV equation with steplike initial data. The focus lies on the Deift-Zhou nonlinear steepest descent analysis in the transition region, where solutions converge to a modulated elliptic (Its-Matveev) solution. We state the corresponding Riemann-Hilbert 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 vector-valued 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.


Speaker:  Mateusz Piorkowski
Institution:  MSRI

Event Organizer:   Ahmad Barhoumi


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