The Ambj?rn-Nielsen-Olesen(ANO) model arises from field theory, in the limiting BPS state, the ANO model is actually a domain wall model which is a basic construct describing a phase transition between two phases. In this paper, we derive a coupled second-order ordinary differential equations of the domain wall model. Then we establish the existence and uniqueness theorem for the domain solutions by using a dynamical shooting method for the parameter γ = 1, and variational method for the parameter γ > 0 and γ = 1.
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