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arXiv · 0712.3105

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

Eiji Onodera
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Abstract

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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Eiji Onodera. 2008-05-20. Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces. https://doi.org/10.3842/sigma.2008.044

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