Motion by curvature of a three-dimensional filament: Similarity solutions (Q1859329)

Summary: 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, \(\nu = \kappa{\mathbf n}\), where \(\mathbf n\) is the principal normal and \(\kappa\) the curvature of the filament. Such formulations are relevant to superconducting vortices and disclinations.