Hasimoto Transformation and Vortex Soliton Motion Driven by Fluid Helicity

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dc.creatorHolm, Darryl D.
dc.creatorStechmann, Samuel N.
dc.date2004-09-20
dc.date.accessioned2026-07-07T05:35:58Z
dc.date.available2026-07-07T05:35:58Z
dc.descriptionVorticity filament motions with respect to the Dirac bracket of Rasetti and Regge [1975] are known to be related to the nonlinear Schrödinger equation by the Hasimoto transformation (HT), when the Hamiltonian is the Local Induction Approximation (LIA) of the kinetic energy. We show that when the Hamiltonian is the LIA of Euler-fluid helicity $\int\mathbf{u}\cdot {\rm curl} \mathbf{u}$, the vorticity filament equation of motion under the Rasetti-Regge Dirac bracket is mapped by HT to the integrable complex modified Korteweg-de Vries (cmKdV) equation, the second equation in the nonlinear Schrödinger hierarchy.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/nlin/0409040
dc.identifierhttp://arxiv.org/abs/nlin/0409040
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80838
dc.subjectExactly Solvable and Integrable Systems
dc.titleHasimoto Transformation and Vortex Soliton Motion Driven by Fluid Helicity
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