Spinning Q-balls for the Klein-Gordon-Maxwell equations
The paper deals with the nonlinear Klein-Gordon-Maxwell equations \(\frac{\partial^2\psi}{\partial t^2} - \nabla\psi +W'(\psi)=0\), where the nonlinear term \(W\) is assumed to be positive and \(W(0)=0\). The vortices in the nonlinear Klein-Gordon equation are often considered in the Physics literature with the name of spinning \(Q\)-balls. The main result of the paper is the proof of existence of spinning \(Q\)-balls for the nonlinear Klein-Gordon-Maxwell equations, that is, three-dimensional vortex-solutions which are finite energy, stationary solutions such that the matter field has a nontrivial angular momentum and the magnetic field looks like the field created by a finite solenoid.
scientific article; zbMATH DE number 5693403
scientific article