Bellazzini, Jacopo and Benci, Vieri and Bonanno, Claudio and Sinibaldi, Edoardo (2013) On the existence of hylomorphic vortices in the nonlinear Klein-Gordon equation. Dynamics of Partial Differential Equations, Vol. 10 (1), p. 1-24. eISSN 2163-7873. Article.
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In this paper we prove the existence of vortices, namely stand-ing waves with non null angular momentum, for the nonlinear Klein-Gordon equation in dimension N ≥ 3. We show with variational methods that the existence of these kind of solutions, that we have called hylomorphic vortices, depends on a suitable energy-charge ratio. Our variational approach turns out to be useful for numerical investigations as well. In particular, some results in dimension N = 2 are reported, namely exemplificative vortex profiles by varying charge and angular momentum, together with relevant trends for vor-tex frequency and energy-charge ratio. The stability problem for hylomorphic vortices is also addressed. In the absence of conclusive analytical results, vor-tex evolution is numerically investigated: the obtained results suggest that, contrarily to solitons with null angular momentum, vortex are unstable.
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