Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces

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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Bibliographic Details
Main Author: Eiji Onodera
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2008-05-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
dispersive flow
Schrödinger map
geometric analysis
moving frame
Hasimoto transform
vortex filament
Online Access:http://www.emis.de/journals/SIGMA/2008/044/
Description
Summary: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.
ISSN:1815-0659

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