Geodesic
An Analytic Approach to $Q$-Balls
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 342-347

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We present the analytic approach for constructing $Q$-ball solutions in the general case of a sixth-order potential. In particular, we show that the symmetrized Woods–Saxon function describes the $Q$-ball profile function. The energy and charge can therefore be evaluated explicitly.
Keywords: nontopological solitons, Noether charge, mechanical analogue. 
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     title = {An {Analytic} {Approach} to $Q${-Balls}},
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T. A. Ioannidou; A. Kouiroukidis; N. D. Vlachos. An Analytic Approach to $Q$-Balls. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 342-347. http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a11/