Abstract
This note is a case study of a general SU(2) gauge vortex model where the two Higgs multiplets are in the adjoint representation of the gauge group and the Higgs potential energy density contains cross interaction terms The vacuum decay of finite-energy solutions is proved and the existence of a non-trivial solution is established. Moreover, for a special choice of the parameter region, the occurrence of a non-linear desingularization phenomenon is observed.
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