  We address the dynamics of magnetic domain walls in ferromagnetic nanowires
under the influence of external time-dependent magnetic fields. We report a new
exact spatiotemporal solution of the Landau-Lifshitz-Gilbert equation for the
case of soft ferromagnetic wires and nanostructures with uniaxial anisotropy.
The solution holds for applied fields with arbitrary strength and time
dependence. We further extend this solution to applied fields slowly varying in
space and to multiple domain walls.
