Title: The KdV equation with steplike initial data and connections with finite-gap solutions
Speaker: Mateusz Piorkowski (KU Leuven)
Speaker's URL: https://sites.google.com/view/mateuszpiorkowski/home
Abstract: The KdV equation is a nonlinear wave equation used, among others, for modeling shallow water waves. In this talk I will focus on the Riemann-Hilbert analysis of the initial value problem for the KdV equation with steplike initial data. It turns out that in the transition region solutions converge to a modulated elliptic wave, i.e., a genus 1 finite-gap solution, also known as an Its--Matveev solution. The emphasis will be on the peculiarities that arise when analyzing this problem using the Deift-Zhou nonlinear steepest descent method for oscillatory Riemann-Hilbert problems. Part of this work has been a collaboration with Iryna Egorova and Gerald Teschl.
URL associated with Seminar: https://u.osu.edu/aots/
