Exact solutions of multi-vortices and false vacuum bubbles in noncommutative Abelian-Higgs theories

We consider the noncommutative Abelian-Higgs theory and construct new type of exact multi-vortex solutions that solve the static equations of motion. They in general do not follow from the BPS equations; only for some specific values of parameters, they satisfy the BPS equations saturating the Bogomolʹnyi bound. We further consider the Abelian-Higgs theory with more complicated scalar potential allowing unstable minima and construct exact solutions of noncommutative false vacuum bubble with integer magnetic flux. The classical stability of the solutions is discussed.