Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces
We study the structure of differential equations of one-dimensional dispersive flows into compact Riemann surfaces. These equations geometrically generalize two-sphere valued systems modeling the motion of vortex filament. We define a generalized Hasimoto transform by constructing a good moving fram...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2008 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148988 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces / E. Onodera // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862531945351610368 |
|---|---|
| author | Onodera, E. |
| author_facet | Onodera, E. |
| citation_txt | Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces / E. Onodera // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the structure of differential equations of one-dimensional dispersive flows into compact Riemann surfaces. These equations geometrically generalize two-sphere valued systems modeling the motion of vortex filament. We define a generalized Hasimoto transform by constructing a good moving frame, and reduce the equation with values in the induced bundle to a complex valued equation which is easy to handle. We also discuss the relationship between our reduction and the theory of linear dispersive partial differential equations.
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| first_indexed | 2025-11-24T04:40:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148988 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:40:14Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Onodera, E. 2019-02-19T12:45:19Z 2019-02-19T12:45:19Z 2008 Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces / E. Onodera // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35Q55; 35Q35; 53Z05 https://nasplib.isofts.kiev.ua/handle/123456789/148988 We study the structure of differential equations of one-dimensional dispersive flows into compact Riemann surfaces. These equations geometrically generalize two-sphere valued systems modeling the motion of vortex filament. We define a generalized Hasimoto transform by constructing a good moving frame, and reduce the equation with values in the induced bundle to a complex valued equation which is easy to handle. We also discuss the relationship between our reduction and the theory of linear dispersive partial differential equations. The author expresses gratitude to Hiroyuki Chihara for several discussions and valuable advice. Also, thanks to the referees for carefully reading the manuscript. The author is supported by the JSPS Research Fellowships for Young Scientists and the JSPS Grant-in-Aid for Scientific Research No.19·3304. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces Article published earlier |
| spellingShingle | Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces Onodera, E. |
| title | Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces |
| title_full | Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces |
| title_fullStr | Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces |
| title_full_unstemmed | Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces |
| title_short | Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces |
| title_sort | generalized hasimoto transform of one-dimensional dispersive flows into compact riemann surfaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148988 |
| work_keys_str_mv | AT onoderae generalizedhasimototransformofonedimensionaldispersiveflowsintocompactriemannsurfaces |