  The behavior of sufficiently regular solutions to semilinear hyperbolic
equations has attracted a great deal of attention in the past decades,
concerning local/global existence, finite time blow-up, critical exponents, and
propagation of singularities. Solutions of lower regularity may exhibit
unexpected (anomalous) propagation of singularities. The purpose of this paper
is to present various striking examples that seemingly have not been addressed
in the literature so far. The key issue is the interpretation of the nonlinear
operations.
