Differential geometry of the vortex filament equation

DOI10.1016/S0393-0440(98)00024-2zbMath0982.37072arXivhep-th/9611073OpenAlexW3104519085WikidataQ115338786 ScholiaQ115338786MaRDI QIDQ1299358

Yukinori Yasui, Norihito Sasaki

Publication date: 23 August 1999

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9611073

zbMATH Keywords

integrabilityvortex filament equation3D incompressible fluidvery thin vortex tube

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20)

Related Items (7)

Integrable motions of curves in \(S^{1} \times \mathbb R\) ⋮ Null curve evolution in four-dimensional pseudo-Euclidean spaces ⋮ Quasi‐Classical Approximation in Vortex Filament Dynamics. Integrable Systems, Gradient Catastrophe, and Flutter ⋮ Poisson brackets associated to the conformal geometry of curves ⋮ Hamiltonian evolution of curves in classical affine geometries ⋮ A Lie algebra structure on variation vector fields along curves in 2-dimensional space forms ⋮ Vortex string dynamics in an external antisymmetric tensor field

Cites Work

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• Differential geometry and integrability of the Hamiltonian system of a closed vortex filament
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• On the theory of recursion operator
• The Schouten bracket and Hamiltonian operators
• Poisson geometry of the filament equation
• Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
• Symmetries and Integrability
• The spectral theory of a functional-difference operator in conformal field theory
• A soliton on a vortex filament

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