Approximation theorem for the self-focusing Nonlinear Schrödinger Equation and for the periodic curves in ${\bf R}^3$

Details Approximation theorem for the self-focusing Nonlinear Schrödinger Equation and for the periodic curves in ${\bf R}^3$ Approximation theorem for the self-focusing Nonlinear Schrödinger Equation and for the periodic curves in ${\bf R}^3$

2000-02-15

arxiv.org/abs/nlin/0002020v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, LaTeX, macroses amssym.tex and elsart.cls are used (elsart.cls is avaliable on http://www.elsevier.nl/locate/latex)

Scientific paper

10.1016/S0167-2789(01)00155-5

It is shown, that any sufficiently smooth periodic solution of the self-focusing Nonlinear Schr\"odinger equation can be approximated by periodic finite-gap ones with an arbitrary small error. As a corollary an analogous result for the motion of closed curves in ${\Bbb R}^3$ guided by the Filament equation is proved. This equation describes the dynamics of very thin filament vortices in a fluid.

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