35 citations · 125 across the 15 of their papers we have counts for
15 papers
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…
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…
How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave
Iryna Egorova, Johanna Michor
We rigorously derive the long-time asymptotics of the Toda shock wave in a middle region where the solution is asymptotically finite gap. In particular, we describe the influence o…
Long-time asymptotics for Toda shock waves in the modulation region
Iryna Egorova, Johanna Michor, Anton Pryimak +1
We show that Toda shock waves are asymptotically close to a modulated finite gap solution in the region separating the soliton and the elliptic wave regions. We previously derived…
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…
Rarefaction Waves for the Toda Equation via Nonlinear Steepest Descent
Iryna Egorova, Johanna Michor, Gerald Teschl
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Toda lattice with steplike initial data corresponding to a rarefaction wave.