2012/11/23 by Jacopo Bellazzini, Vieri Benci, Bellazzini, Jacopo +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1211.5553
openalex publication_date 2012/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove the existence of vortices, namely standing waves with\nnon null angular momentum, for the nonlinear Klein-Gordon equation in dimension\nN\≥ 3. We show with variational methods that the existence of these kind of\nsolutions, that we have called \hylomorphic vortices, depends on a\nsuitable energy-charge ratio. Our variational approach turns out to be useful\nfor numerical investigations as well. In particular, some results in dimension\nN=2 are reported, namely exemplificative vortex profiles by varying charge and\nangular momentum, together with relevant trends for vortex frequency and\nenergy-charge ratio. The stability problem for hylomorphic vortices is also\naddressed. In the absence of conclusive analytical results, vortex evolution is\nnumerically investigated: the obtained results suggest that, contrarily to\nsolitons with null angular momentum, vortex are unstable.\n