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

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