  Tachyons or hypothetical faster-than-light (FTL) particles would fail the
principle of causality. Such particles may only be imagined when they have no
energy and momentum and, thus, no observable interaction. In this paper, we
show that the classical relativistic field theory with non-standard Lagrangian
densities (k-field models) does not rule out the existence of FTL particle-like
solutions (solitons) with zero energy and momentum in 3+1 dimensions. However,
contrary to our expectation, we show that it is possible to have k-field models
that lead to energetic FTL soliton solutions in 3+1 dimensions.
