Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces
Analysis of PDEs
2008-05-20 v2
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.
Keywords
Cite
@article{arxiv.0712.3105,
title = {Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces},
author = {Eiji Onodera},
journal= {arXiv preprint arXiv:0712.3105},
year = {2008}
}
Comments
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/