Construction of KdV Flow I. τ-Function via Weyl Function
Sato introduced the τ-function to describe solutions to a wide class of completely integrable differential equations. Later Segal–Wilson represented it in terms of the relevant integral operators on Hardy space of the unit disc. This paper gives another representation of the τ -functions by the Weyl...
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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2018
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| Schriftenreihe: | Журнал математической физики, анализа, геометрии |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/145877 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Construction of KdV Flow I. τ-Function via Weyl Function / Shinichi Kotani // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 3. — С. 297-335. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Sato introduced the τ-function to describe solutions to a wide class of completely integrable differential equations. Later Segal–Wilson represented it in terms of the relevant integral operators on Hardy space of the unit disc. This paper gives another representation of the τ -functions by the Weyl functions for 1d Schrödinger operators with real valued potentials, which will make it possible to extend the class of initial data for the KdV equation to more general one. |
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