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

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 ${\mathbb{R}}^3$ guided by the Filament equation is proved. This equation describes the dynamics of very thin filament vortices in a fluid.

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

References in corpus (2)

• Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations
• Closed curves in R^3: a characterization in terms of curvature and torsion, the Hasimoto map and periodic solutions of the Filament Equation

Cited by in corpus (6)

• Fast Numerical Nonlinear Fourier Transforms
• An integrable hierarchy with a perturbed Henon-Heiles system
• Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations
• On closed finite gap curves in spaceforms II
• On Closed Finite Gap Curves in Spaceforms I
• Notes on dispersionful and dispersionless vortex filament equations in 1+1 and 2+1 dimensions