  We show that domain walls, or kinks, can be constructed in simple scalar
theories where the scalar has no potential. These theories belong to a class of
k-essence where the Lagrangian vanishes identically when one lets the
derivatives of the scalar vanish. The domain walls we construct have positive
energy and stable quadratic perturbations. As particular cases, we find
families of theories with domain walls and their quadratic perturbations
identical to the ones of the canonical Mexican hat or sine-Gordon scalar
theories. We show that canonical and non canonical cases are nevertheless
distinguishable via higher order perturbations or a careful examination of the
energies. In particular, in contrast to the usual case, our walls are local
minima of the energy among the field configuration having some fixed
topological charge, but not global minima.
