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math.CV2019
Riemann-Hilbert Theory without local Parametrix Problems: Applications to Orthogonal Polynomials
Mateusz Piorkowski
We study whether in the setting of the Deift-Zhou nonlinear steepest descent method one can avoid solving local parametrix problems explicitly, while still obtaining asymptotic res…
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…
nlin.SI2019
Asymptotics of KdV shock waves via the Riemann-Hilbert approach
Iryna Egorova, Mateusz Piorkowski, Gerald Teschl
This paper discusses some general aspects and techniques associated with the long-time asymptotics of steplike solutions of the Korteweg--de Vries (KdV) equation via vector Riemann…