1972/02/08 by Hidenori Hasimoto · 1,003 citations
Physics and Astronomy · Computer Science · Mathematics · #Nonlinear Photonic Systems #Nonlinear Dynamics and Pattern Formation #Nonlinear Waves and Solitons #Physics #Inviscid flow #Curvature #Protein filament #Vortex #Soliton #Mathematical physics #Compressibility #Classical mechanics #Geometry #Mechanics #Mathematics #Materials science #Quantum mechanics
paper · doi:10.1017/s0022112072002307
published in Journal of Fluid Mechanics 51(3), 477-485 (Cambridge University Press)
openalex publication_date 1972/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The intrinsic equation governing the curvature K and the torsion τ of an isolated very thin vortex filament without stretching in an incompressible inviscid fluid is reduced to a non-linear Schrödinger equation \frac\rm li(∂ ψ)/(∂ t) = (∂2ψ)/(∂ s2)+\textstyle(1)/(2)(|ψ|2+A)ψ, where t is the time, s the length measured along the filament, ψ is the complex variable ψ = κexp(i∫0sτ ds) and is a function oft. It is found that this equation yields a solution describing the propagation of a loop or a hump of helical motion along a line vortex, with a constant velocity 2τ. The relation to the system of intrinsic equations derived by Betchov (1965) is discussed.