Motion by curvature of a three-dimensional filament: similarity solutions

Abstract

We systematically classify and investigate fully three-dimensional similarity solutions to a system of equations describing the motion of a filament moving in the direction of its principal normal with velocity proportional to its curvature, [ngr] = [kgr]n, where n is the principal normal and [kgr] the curvature of the filament. Such formulations are relevant to superconducting vortices and disclinations.