## Three dimensional vortices in the nonlinear wave equation.(English)Zbl 1178.35263

The authors prove the existence of solitary waves with non-vanishing angular momentum for the equation $$\psi _{tt}-\Delta \psi+W'(\psi )=0,$$ where $$W$$ is a nonnegative potential depending only on $$\left|\psi \right|.$$ The proof relies on finding nonnegative cylindrical solutions to a standing equation with suitable integrability properties. The results will be useful to many physical problems.

### MSC:

 35L71 Second-order semilinear hyperbolic equations 35Q51 Soliton equations 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35J60 Nonlinear elliptic equations