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.
|Number of pages||17|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 1996 Apr|
ASJC Scopus subject areas
- Applied Mathematics