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Bogomol'nyi-Prasad-Sommerfield solitons in models with spontaneously brokengauge symmetry have been intensively studied at infinite gauge coupling limit,where the governing equation -- so-called master equation -- is exactlysolvable. Except for a handful of special solutions, the standing impression isthat analytic results at finite coupling are generally unavailable. The aim ofthis paper is to demonstrate, using domain walls in Abelian-Higgs models as thesimplest example, that exact solitons at finite gauge coupling can be readilyobtained if the number of Higgs fields ($N_F$) is large enough. In particular,we present a family of exact solutions, describing $N$ domain walls atarbitrary positions in models with at least $N_F \geq 2N+1$. We have also foundthat adding together any pair of solution can produce a new exact solution ifthe combined tension is below a certain limit.

Exact BPS domain walls at finite gauge coupling