Badiale, Marino; Benci, Vieri; Rolando, Sergio Three dimensional vortices in the nonlinear wave equation. (English) Zbl 1178.35263 Boll. Unione Mat. Ital. (9) 2, No. 1, 105-134 (2009). 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. Reviewer: Marie Kopáčková (Praha) Cited in 9 Documents 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 Keywords:solitary wave; angular momentum; Klein-Gordon equation; classical solution PDF BibTeX XML Cite \textit{M. Badiale} et al., Boll. Unione Mat. Ital. (9) 2, No. 1, 105--134 (2009; Zbl 1178.35263) OpenURL