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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
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