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.
Cite this article
Giles W. Richardson, John R. King, Motion by curvature of a three-dimensional filament: similarity solutions. Interfaces Free Bound. 4 (2002), no. 4, pp. 395–421DOI 10.4171/IFB/67