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We prove the existence of rotating solitary waves (vortices) with enough largely prescribed L 2  norm for the nonlinear Klein-Gordon equation with nonnegative potential, which makes the equation suitable for physical models and guarantees the well-posedness of the corresponding Cauchy problem. This is done by finding nonnegative cylindrical solutions to the standing equation

Vortices with Prescribed L 2 Norm in the Nonlinear Wave Equation