Backlund transformations and knots of constant torsion

Details Backlund transformations and knots of constant torsion Backlund transformations and knots of constant torsion

1996-08-07

arxiv.org/abs/dg-ga/9608001v1

Mathematics

Differential Geometry

AMSTeX, 29 pages, 5 Postscript figures, uses BoxedEPSF.tex (all necessary files are included in backlund.tar.gz)

Scientific paper

The Backlund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constant torsion. We study its effects on closed curves (in particular, elastic rods) that generate multiphase solutions for the vortex filament flow (also known as the Localized Induction Equation). In doing so, we obtain analytic constant-torsion representatives for a large number of knot types.

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