Integrable Systems and Random Matrix Theory Seminar

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)