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A Paley-Wiener Theorem for Periodic Scattering with Applications to the Korteweg-de Vries Equation
A one-dimensional SchrÄodinger operator which is a short-range perturbation of a finite-gap operator is considered. There are given the necessary and su±cient conditions on the left/right reflection coeffcient such that the difference of the potentials has finite support to the left/right, respectiv...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2010
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| Series: | Журнал математической физики, анализа, геометрии |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/106630 |
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| Summary: | A one-dimensional SchrÄodinger operator which is a short-range perturbation of a finite-gap operator is considered. There are given the necessary and su±cient conditions on the left/right reflection coeffcient such that the difference of the potentials has finite support to the left/right, respectively. Moreover, these results are applied to show a unique continuation type result for solutions of the Korteweg{de Vries equation in this context. By virtue of the Miura transform an analogous result for the modified Korteweg-de Vries equation is also obtained. |
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