Domain Wall Solution Arising in Abelian Higgs Model Subject to Born-Infeld Theory of Electrodynamics

In this note we research the Abelian Higgs model subject to the Born-Infeld theory of electrodynamics for which the BPS equations can be reduced into a quasi-linear differential equation. We show that the equation exists a unique solution under two interesting boundary conditions which realize the corresponding phase transition. We construct the solution through a dynamical shooting method for which the correct shooting slope is unique. We also obtain the sharp asymptotic estimate for the solution at infinity.