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.
Reviewer: Marie Kopáčková (Praha)
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 |