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Integrable Systems and Random Matrix Theory Seminar

Long-time asymptotics of KdV dispersive shock wave via Riemann-Hilbert problems
Monday, September 13, 2021
3:30-4:30 PM
ZOOM ID: 922 9373 3366 Passcode: 651935 Off Campus Location
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. Speaker(s): Mateusz Piorkowski (University of Vienna)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics