A Riemann - Hilbert problem for an energy dependent Schrödinger operator
- 1 December 1996
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 12 (6) , 1003-1025
- https://doi.org/10.1088/0266-5611/12/6/014
Abstract
We consider an inverse scattering problem for Schrödinger 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. Dedicated to Hugh Turrittin on his 90th birthdayKeywords
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