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

Badiale, Marino; Benci, Vieri; Rolando, Sergio

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)

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