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

Piotr G. Grinevich
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Abstract

It is shown, that any sufficiently smooth periodic solution of the self-focusing Nonlinear Schrödinger 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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Piotr G. Grinevich. 2000-02-15. Approximation theorem for the self-focusing Nonlinear Schrödinger Equation and for the periodic curves in ${\bf R}^3$. https://doi.org/10.1016/s0167-2789(01)00155-5

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