4 papers
The Hasimoto Transformation for a Finite Length Vortex Filament and its Application
Masashi Aiki
We consider two nonlinear equations, the Localized Induction Equation and the cubic nonlinear Schrödinger Equation, and prove that the solvability of certain initial-boundary value…
Head-On Collision of a Pair of Coaxial Circular Vortex Filament
Masashi Aiki
We consider the head-on collision of two coaxial vortex rings described as the motion of two circular vortex filaments under the localized induction approximation. We prove the exi…
On the Existence of Leapfrogging Pair of Circular Vortex Filaments
Masashi Aiki
We propose and analyze a system of nonlinear partial differential equations describing the motion of a pair of vortex filaments. Furthermore, for a pair of coaxial circular vortex…
Motion of a Vortex Filament with Axial Flow in the Half Space
Masashi Aiki, Tatsuo Iguchi
We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensiona…