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Differential Geometry and Integrability of the Hamiltonian System of a Closed Vortex Filament

Norihito Sasaki
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Abstract

The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequense of constants of motion in involution. An algebraic framework is given for the aim of describing differential geometry of this system. A geometrical structure related to the integrability of this system is revealed. It is not a bi-Hamiltonian structure but similar one. As a related topic, a remark on the inspection of J.Langer and R.Perline, J.Nonlinear Sci.1, 71 (1991), is given.

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Norihito Sasaki. 1996-03-29. Differential Geometry and Integrability of the Hamiltonian System of a Closed Vortex Filament. https://arxiv.org/abs/hep-th/9510172

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