Some stationary properties of a $Q$-ball in arbitrary space dimensions
  Introducing new physically motivated ans\"{a}tze, we explore both analytically and numerically the classical and absolute stabilities of a single $Q$-ball in an arbitrary number of spatial dimensions $D$, working in both the thin and thick wall limits. 
Mitsuo I. Tsumagari, Edmund J. Copeland, Paul M. Saffin