On Closed Finite Gap Curves in Spaceforms I

Abstract

We show that the spaces of closed finite gap curves in ${\mathbb{R}}^3$ and ${\mathbb{S}}^3$ are dense with respect to the Sobolev $W^{2,2}$-norm in the spaces of closed curves in ${\mathbb{R}}^3$ respectively ${\mathbb{S}}^3$.

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• The finite gap method and the periodic NLS Cauchy problem of the anomalous waves, for a finite number of unstable modes
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• Singular curves and Baker-Akhiezer functions
• Spectral data for simply-periodic solutions of the sinh-Gordon equation
• On closed finite gap curves in spaceforms II

Cited by in corpus (1)

• On closed finite gap curves in spaceforms II