Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations

Maria J. Esteban*, Vladimir Georgiev, Eric Séré

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

91 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)265-281
Number of pages17
JournalCalculus of Variations and Partial Differential Equations
Issue number3
Publication statusPublished - 1996 Apr
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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