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On the existence of stable charged Q-balls. (English) Zbl 1272.35173

Summary: This paper concerns hylomorphic solitons, namely, stable, solitary waves whose existence is related to the ratio energy/charge. In theoretical physics, the name Q-ball refers to a type of hylomorphic solitons or solitary waves relative to the nonlinear Klein-Gordon equation. We are interested in the existence of charged Q-balls, namely, Q-balls for the nonlinear Klein-Gordon equation coupled with the Maxwell equations. In this case, the charge reduces to the electric charge. The main result of this paper establishes that stable, charged Q-balls exist provided that the interaction between the matter and the gauge field is sufficiently small. {
©2011 American Institute of Physics}

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
35Q61 Maxwell equations
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References:

[1] Badiale M., Rend. Semin. Mat Univ. Pol. Torino 62 pp 107– (2004)
[2] DOI: 10.1515/ans-2010-0211 · Zbl 1200.35248
[3] DOI: 10.4310/DPDE.2009.v6.n4.a2 · Zbl 1194.35096
[4] DOI: 10.1007/s00032-009-0105-8 · Zbl 1205.35040
[5] DOI: 10.1007/s11784-006-0008-z · Zbl 1122.35121
[6] Benci V., Adv. Nonlinear Stud. 3 pp 327– (2008)
[7] Benci V., Rend. Lincei Mat. Appl. 20 pp 243– (2009)
[8] DOI: 10.1007/s00220-010-0985-z · Zbl 1194.78009
[9] DOI: 10.3934/dcds.2010.28.875 · Zbl 1205.37081
[10] DOI: 10.1007/s12210-010-0106-0
[11] Berestycki H., Arch. Rational Mech. Anal. 82 pp 313– (1983)
[12] DOI: 10.1016/j.na.2009.10.004 · Zbl 1183.35232
[13] DOI: 10.1016/0550-3213(85)90286-X
[14] Coleman S., Nucl. Phys. (erratum) 269 pp 744– (1986)
[15] DOI: 10.1007/BF01976040 · Zbl 0496.35061
[16] Gelfand I. M., Calculus of Variations (1963)
[17] DOI: 10.1215/S0012-7094-94-07402-4 · Zbl 0818.35123
[18] DOI: 10.1016/j.anihpc.2010.02.001 · Zbl 1194.35378
[19] DOI: 10.1007/BF02103714 · Zbl 0858.35122
[20] Rajaraman R., Solitons and Instantons (1989)
[21] DOI: 10.1063/1.1664693
[22] DOI: 10.1007/BF01208779 · Zbl 0539.35067
[23] Vilenkin A., Cambridge Monographs on Mathematical Physics (1994)
[24] Yang Y., Solitons in Field Theory and Nonlinear Analysis (2000)
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