期刊
DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS
卷 10, 期 1, 页码 1-24出版社
INT PRESS BOSTON, INC
关键词
Hylomorphic vortices; Klein-Gordon equation; angular momentum
资金
- MIUR, Italy [PRIN2009]
- King Saud University, Riyadh, Saudi Arabia
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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