dorsal/arxiv
View SchemaA Riemann-Hilbert Problem for an Energy Dependent Schr\"odinger Operator
| Authors | David H. Sattinger, Jacek Szmigielski |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9712013 |
| URL | https://arxiv.org/abs/solv-int/9712013 |
| DOI | 10.1088/0266-5611/12/6/014 |
| Journal | Inverse Problems 12 (1996) 1003-1025 |
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 $u_t+(u^2/2+w)_x=0, w_t\pm u_{xxx}+(uw)_x=0$ for suitably restricted, complementary classes of initial data.
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"abstract": "\\We consider an inverse scattering problem for Schr\\\"odinger operators with\nenergy dependent potentials. The inverse problem is formulated as a\nRiemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for\ntwo distinct symmetry classes. As an application we prove global existence\ntheorems for the two distinct systems of partial differential equations\n$u_t+(u^2/2+w)_x=0, w_t\\pm u_{xxx}+(uw)_x=0$ for suitably restricted,\ncomplementary classes of initial data.",
"arxiv_id": "solv-int/9712013",
"authors": [
"David H. Sattinger",
"Jacek Szmigielski"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0266-5611/12/6/014",
"journal_ref": "Inverse Problems 12 (1996) 1003-1025",
"title": "A Riemann-Hilbert Problem for an Energy Dependent Schr\\\"odinger Operator",
"url": "https://arxiv.org/abs/solv-int/9712013"
},
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