On Closed Finite Gap Curves in Spaceforms I

Symmetry Integrability and Geometry-Methods and Applications

article

Sebastian Klein¹  Martin Kilian² 

[1] Lehrstuhl für Mathematik III, Universität Mannheim;Department of Mathematics, University College Cork

关键词: closed finite gap curves;    integrable systems;    nonlinear Schr¨odinger equation;    asymptotic estimates;   

DOI  :  10.3842/SIGMA.2020.011

来源: National Academy of Science of Ukraine

【 摘 要 】

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 ${\mathbb S}^3$.

【 授权许可】

Unknown