Phase Transition Solutions In Intrinsically Geometric Domain Wall Models

In this paper, we discuss domain walls which are topological solitons in one spacedimension. We present a study on the existence of the solutions of the basic governingequations in intrinsically geometric domain wall models. When the cross section andpotential density are both even, we establish the existence of an odd domain wall solutionrealizing the phase transition process between two adjacent domain phases. Our method isbased on a dynamical shooting approach which provides an e?ective framework for domainwall solution. When the cross section and potential density are not assumed to be evenfunctions, we will establish the existence of a domain wall solution via direct minimization.