Rarefaction waves and dispersive shock waves are generated from the step-like initial data
in many nonlinear evolution equations including the classical example of the Korteweg–de …

The paper aims at develo** the Riemann–Hilbert (RH) approach for the modified
Camassa–Holm (mCH) equation on the line with non-zero boundary conditions, in the case …

Abstract In the Korteweg–de Vries equation (KdV) context, we put forward a continuous
version of the binary Darboux transformation (aka the double commutation method). Our …

This Thesis aims at the development of the Inverse Scattering Transform (IST), in the form of
a Riemann–Hilbert problem, for the modified Camassa–Holm (mCH) equation 𝑚𝑡+(︀ (𝑢 2 …

Abstract The Korteweg–de Vries (KdV) equation is a classical model for describing long
surface gravity waves propagating in dispersive media. It is known to possess many families …

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 …

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 …