4.2 Article

On the existence of hylomorphic vortices in the nonlinear Klein-Gordon equation

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出版社

INT PRESS BOSTON, INC

关键词

Hylomorphic vortices; Klein-Gordon equation; angular momentum

资金

  1. MIUR, Italy [PRIN2009]
  2. King Saud University, Riyadh, Saudi Arabia

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In this paper we prove the existence of vortices, namely standing 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 vortex frequency and energy-charge ratio. The stability problem for hylomorphic vortices is also addressed. In the absence of conclusive analytical results, vortex evolution is numerically investigated: the obtained results suggest that, contrarily to solitons with null angular momentum, vortex are unstable.

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