A Riemann - Hilbert problem for an energy dependent Schrödinger operator
David H Sattinger; Jacek Szmigielski; David H Sattinger; University of Minnesota, Minneapolis, Minnesota 55455, USA; the University of Saskatchewan, Saskatoon, Saskatchewan, Canada; Jacek Szmigielski; University of Minnesota, Minneapolis, Minnesota 55455, USA; the University of Saskatchewan, Saskatoon, Saskatchewan, Canada
Журнал:
Inverse Problems
Дата:
1996-12-01
Аннотация:
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 birthday
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