On self-similar solutions of the vortex filament equation

Autor:	Gamayun, O., Lisovyy, O.
Rok vydání:	2019
Předmět:	Mathematical Physics Condensed Matter - Strongly Correlated Electrons Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
DOI:	10.1063/1.5096170
Popis:	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. Comment: 15 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1903.02105 Zobrazit plný text záznamu View this record from Arxiv