Spinning Q-balls in Abelian Gauge Theories with positive potentials:   existence and non existence
  We study the existence of cylindrically symmetric electro-magneto-static solitary waves for a system of a nonlinear Klein-Gordon equation coupled with Maxwell's equations in presence of a positive mass and of a nonnegative nonlinear potential. Nonexistence results are provided as well. 
Dimitri Mugnai and Matteo Rinaldi
math.AP