  We study the nonlinear excitations of a vortex-line in a Bose-Einstein
condensate trapped in a one-dimensional optical lattice. We find that the
classical Euler dynamics of the vortex results in a description of the vortex
line in terms of a (discrete) one-dimensional Gross-Pitaevskii equation, which
allows for both bright and gray soliton solutions. We discuss these solutions
in detail and predict that it is possible to create vortex-line solitons with
current experimental capabilities.
