The Hasimoto transformation and integrable flows on curves

DOI10.1016/0893-9659(90)90015-4zbMath0714.44003OpenAlexW1969899916WikidataQ128054474 ScholiaQ128054474MaRDI QIDQ750811

Joel C. Langer, Ron Perline

Publication date: 1990

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0893-9659(90)90015-4

zbMATH Keywords

nonlinear Schrödinger equationfilament equationHamiltonian vector fieldsdifferentialfilament flowHasimoto transformationintegrable flows on curves

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Transform methods (e.g., integral transforms) applied to PDEs (35A22) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (8)

A different modelling of complex Hasimoto map for pseudo-null curves via Bishop frame ⋮ Hasimoto surfaces for two classes of curve evolution in Minkowski 3-space ⋮ Localized induction hierarchy and Weingarten systems ⋮ Geometric integration of the Betchov-Da Rios equation in a gravity-electromagnetism unified model ⋮ A class of vortex filament solitons in fluids, plasmas, and superconductors ⋮ Unnamed Item ⋮ Moving non-null curves according to Bishop frame in Minkowski 3-space ⋮ Poisson geometry of the filament equation

Cites Work

• Unnamed Item
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• The total squared curvature of closed curves
• Poisson geometry of the filament equation
• Knotted Elastic Curves in R ³
• A soliton on a vortex filament

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