arXiv subjects

Till Luc Lange

Publications and source records attributed to Till Luc Lange.

2 recordsLinked to original sources

arXiv2016

Rarefaction Waves of the Korteweg-de Vries Equation via Nonlinear Steepest Descent

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation with steplike initial data leading to a rarefaction wave. In addition to the leading asymptotic we also compute the next term in the asymptotic expansion of the rarefaction wave, which was not known before.

nlin.SI↗

arXiv2015

Inverse scattering theory for Schrödinger operators with steplike potentials

We study the direct and inverse scattering problem for the one-dimensional Schrödinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed smoothness and prescribed decay to their asymptotics. These results are important for solving the Korteweg-de Vries equation via the inverse scattering transform.

math.SP↗