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

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

1995-10-24

arxiv.org/abs/hep-th/9510172v3

Lett.Math.Phys. 39 (1997) 229-241

Physics

High Energy Physics

High Energy Physics - Theory

Title is changed ('a' is added). A mistake (absence of stating F-linearity condition of a skew-adjoint op., Sect.4) is correct

Scientific paper

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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