This article is cited in 12 papers

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

Eiji Onodera

Mathematical Institute, Tohoku University, Sendai 980-8578, Japan

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 inear dispersive partial differential equations.

Keywords: dispersive flow; Schrödinger map; geometric analysis; moving frame; Hasimoto transform; vortex filament.

MSC: 35Q55; 35Q35; 53Z05

Received: December 18, 2007; in final form May 14, 2008; Published online May 20, 2008

Language: English

DOI: 10.3842/SIGMA.2008.044

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ArXiv: 0712.3105