  We argue that topological compactons (solitons with compact support) may be
quite common objects if $k$-fields, i.e., fields with nonstandard kinetic term,
are considered, by showing that even for models with well-behaved potentials
the unusual kinetic part may lead to a power-like approach to the vacuum, which
is a typical signal for the existence of compactons. The related approximate
scaling symmetry as well as the existence of self-similar solutions are also
discussed. As an example, we discuss domain walls in a potential Skyrme model
with an additional quartic term, which is just the standard quadratic term to
the power two. We show that in the critical case, when the quadratic term is
neglected, we get the so-called quartic $\phi^4$ model, and the corresponding
topological defect becomes a compacton. Similarly, the quartic sine-Gordon
compacton is also derived. Finally, we establish the existence of topological
half-compactons and study their properties.
