Summary
The Hasimoto transformation (relating vortex filament flow to the nonlinear Schrödinger equation) is interpreted in the context of Poisson geometry with the aid of a compact formula for its differential. A useful relationship is derived between Killing fields for soliton solutions of the filament flow and the sequence of commuting Hamiltonian flows.
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Communicated by Jerrold Marsden
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Langer, J., Perline, R. Poisson geometry of the filament equation. J Nonlinear Sci 1, 71–93 (1991). https://doi.org/10.1007/BF01209148
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DOI: https://doi.org/10.1007/BF01209148