Lund–Regge vortex strings in terms of Weierstrass elliptic functions

Abstract

We study quasi-periodic solutions of the Lund–Regge model in terms of the elliptic functions of Weierstrass. They describe the Kida-class motions of relativistic strings in an external antisymmetric tensor field. Our solution includes various vortex string shapes such as the closed vortex ring, the helicoidal filament, the generalized Zee's solution and the Hasimoto type 1-soliton filament.