THE LOCALIZED INDUCTION HIERARCHY AND THE LUND-REGGE EQUATION

An evolution equation of a curve is constructed by summing up the infi nite sequence of commuting vector fields of the integrable hierarchy f or the localized induction equation (LIE). It is shown to be equivalen t to the Lund-Regge equation. The intrinsic equations governing the cu rvature and torsion are deduced in the form of integrodifferential evo lution equations. A class of exact solutions which correspond to the p ermanent forms of a curve evolving by a steady rigid motion are presen ted. The analysis of the solutions reveals that, given the shape, ther e are two speeds of motion, one of which has no counterpart in the cas e of the LIE.