Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations
Esteban, Maria J.; Georgiev, Vladimir; Séré, Eric (1996), Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations, Calculus of Variations and Partial Differential Equations, 4, 3, p. 265-281. http://dx.doi.org/10.1007/BF01254347
TypeArticle accepté pour publication ou publié
Journal nameCalculus of Variations and Partial Differential Equations
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Abstract (EN)The Maxwell-Dirac system describes the interaction of an electron with its own electromagnetic field. We prove the existence of soliton-like solutions of Maxwell-Dirac in (3+1)-Minkowski space-time. The solutions obtained are regular, stationary in time, and localized in space. They are found by a variational method, as critical points of an energy functional. This functional is strongly indefinite and presents a lack of compactness. We also find soliton-like solutions for the Klein-Gordon-Dirac system, arising in the Yukawa model.
Subjects / KeywordsKlein-Gordon-Dirac system; soliton-like solutions; Maxwell-Dirac system
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