On generalized geometric domain-wall models

We study domain walls that are topological solitons in one dimension. We present an existence theory for the solutions of the basic governing equations of some extended geometrically constrained domain-wall models. When the cross-section and potential density are both even, we establish the existence of an odd domain-wall solution realizing the phase-transition process between two adjacent domain phases. When the cross-section satisfies a certain integrability condition, we prove that a domain-wall solution always exists that links two arbitrarily designated domain phases.