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Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces
Репозиторій DSpace/Manakin
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces
Інший ID:
2000 Mathematics Subject Classification: 35Q55; 35Q35; 53Z05
Посилання:
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.
Підтримка:
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.
Дата:
2008
Переглядів:
501
Завантажень:
232
Анотація:
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.
