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On self-similar solutions of the vortex filament equation

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 the σ-Painlevé IV equation with two real parameters. Connection formulae for Painlevé 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.
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Submitted on : Tuesday, September 24, 2019 - 11:14:32 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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O. Gamayun, O. Lisovyy. On self-similar solutions of the vortex filament equation. J.Math.Phys., 2019, 60 (8), pp.083510. ⟨10.1063/1.5096170⟩. ⟨hal-02296213⟩



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