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The planar filament equation

Joel Langer·Ron Perline
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Abstract

The planar filament equation and its relation to the modified Korteweg-deVries equation are studied in the context of Poisson geometry. The structure of the planar filament equation is shown to be similar to that of the 3-D localized induction equation, previously studied by the authors.

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Joel Langer, Ron Perline. 1994-03-25. The planar filament equation. https://arxiv.org/abs/solv-int/9403001

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