  We investigate models described by real scalar fields, searching for defect
structures in the presence of interactions which explicitly violate Lorentz and
CPT symmetries. We first deal with a single field, and we investigate a class
of models which supports traveling waves that violate Lorentz invariance. This
scenario is then generalized to the case of two (or more) real scalar fields.
In the case of two fields, in particular, we introduce another class of models,
which supports topological structures that attain a Bogomol'nyi bound, although
violating both Lorentz and CPT symmetries. An example is considered, for which
we construct the Bogomol'nyi bound and find some explicit solutions. We show
that violation of both Lorentz and CPT symmetries induces the appearance of an
asymmetry between defects and anti-defects, including the presence of linearly
stable solutions with negative energy density in their outer side.
