Mathematics – Differential Geometry
Scientific paper
1997-03-26
Mathematics
Differential Geometry
LaTeX, 27 pages, macros "amssym.def" used
Scientific paper
If a curve in R^3 is closed, then the curvature and the torsion are periodic functions satisfying some additional constraints. We show that these constraints can be naturally formulated in terms of the spectral problem for a 2x2 matrix differential operator. This operator arose in the theory of the self-focusing Nonlinear Schrodinger Equation. A simple spectral characterization of Bloch varieties generating periodic solutions of the Filament Equation is obtained. We show that the method of isoperiodic deformations suggested earlier by the authors for constructing periodic solutions of soliton equations can be naturally applied to the Filament Equation.
Grinevich Petr G.
Schmidt Martin Ulrich
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