Domain walls without a potential

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