  We study large deviations for the current of one-dimensional stochastic
particle systems with periodic boundary conditions. Following a recent approach
based on an earlier result by Jensen and Varadhan, we compare several
candidates for atypical currents to travelling wave density profiles, which
correspond to non-entropic weak solutions of the hyperbolic scaling limit of
the process. We generalize previous results to partially asymmetric systems and
systems with convex as well as concave current-density relations, including
zero-range and inclusion processes. We provide predictions for the large
deviation rate function covering the full range of current fluctuations using
heuristic arguments, and support them by simulation results using cloning
algorithms wherever they are computationally accessible. For partially
asymmetric zero-range processes we identify an interesting dynamic phase
transition between different strategies for atypical currents, which is of a
generic nature and expected to apply to a large class of particle systems on a
ring.
