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

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

2007-12-19

arxiv.org/abs/0712.3105v2

SIGMA 4 (2008), 044, 10 pages

Mathematics

Analysis of PDEs

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2008.044

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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