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• W3105270872 abstract "We study self-similar solutions of the binormal curvature flow which governs the evolution of vortex filaments and is equivalent to the Landau-Lifshitz equation. The corresponding dynamics is described by the real solutions of $sigma$-Painlev'{e} IV equation with two real parameters. Connection formulae for Painlev'{e} IV transcendents allow for a complete characterization of the asymptotic properties of the curvature and torsion of the filament. We also provide compact hypergeometric expressions for self-similar solutions corresponding to corner initial conditions." @default.
• W3105270872 created "2020-11-23" @default.
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• W3105270872 date "2019-08-01" @default.
• W3105270872 modified "2023-10-15" @default.
• W3105270872 title "On self-similar solutions of the vortex filament equation" @default.
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• W3105270872 doi "https://doi.org/10.1063/1.5096170" @default.
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