Vortex string dynamics in an external antisymmetric tensor field

We study the Lund-Regge equation that governs the motion of strings in a co nstant background antisymmetric tensor field by using the duality between t he Lund-Regge equation and the complex sine-Gordon equation. Similar to the cases of vortex filament configurations in fluid dynamics, we find various exact solitonic string configurations which are the analogue of the Kelvin wave, the Hasimoto soliton and the smoke ring. In particular, using the du ality relation, we obtain a completely new type of configuration which corr esponds to the breather of the complex sine-Gordon equation. (C) 1999 Elsev ier Science B.V. All rights reserved.