A Riemann-Hilbert Problem for an Energy Dependent Schr\"odinger Operator
solv-int
2009-10-30 v1 Exactly Solvable and Integrable Systems
Abstract
\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct symmetry classes. As an application we prove global existence theorems for the two distinct systems of partial differential equations for suitably restricted, complementary classes of initial data.
Cite
@article{arxiv.solv-int/9712013,
title = {A Riemann-Hilbert Problem for an Energy Dependent Schr\"odinger Operator},
author = {David H. Sattinger and Jacek Szmigielski},
journal= {arXiv preprint arXiv:solv-int/9712013},
year = {2009}
}