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math.AP2022
Soliton asymptotics for the KdV shock problem of low regularity
Iryna Egorova, Johanna Michor, Gerald Teschl
We revisit the asymptotic analysis of the KdV shock problem in the soliton region. Our approach is based on the analysis of the associated Riemann-Hilbert problem and we extend the…
math.AP2021
Soliton asymptotics for KdV shock waves via classical inverse scattering
Iryna Egorova, Johanna Michor, Gerald Teschl
We show how the inverse scattering transform can be used as a convenient tool to derive the long-time asymptotics of shock waves for the Korteweg-de Vries (KdV) equation in the sol…
math.AP2018★ 19 cited
Explicit solutions for nonlocal NLS: GBDT and algebro-geometric approaches
J. Michor, A. L. Sakhnovich
We apply the GBDT version of the Bäcklund-Darboux transformation to the nonlocal NLS (focusing and defocusing cases). The matrix case is included and solutions in the form of recta…