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math.AP2021
A scalar Riemann-Hilbert problem on the torus: Applications to the KdV equation
Mateusz Piorkowski, Gerald Teschl
We take a closer look at the Riemann-Hilbert problem associated to one-gap solutions of the Korteweg-de Vries equation. To gain more insight, we reformulate it as a scalar Riemann-…
math.AP2019
Parametrix problem for the Korteweg--de Vries equation with steplike initial data
Mateusz Piorkowski
In this paper we study the asymptotics of solutions to the Korteweg--de Vries equation with steplike initial data, which lead to shock waves in the region between the asymptoticall…