Geodesic
Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 inear dispersive partial differential equations.
Keywords: dispersive flow; Schrödinger map; geometric analysis; moving frame; Hasimoto transform; vortex filament. 
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     author = {Eiji Onodera},
     title = {Generalized {Hasimoto} {Transform} of {One-Dimensional} {Dispersive} {Flows} into {Compact} {Riemann} {Surfaces}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a43/}
}
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Eiji Onodera. Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a43/

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