Calculus of Variations and Partial Differential Equations

, Volume 4, Issue 3, pp 265–281

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

  • Maria J. Esteban
  • Vladimir Georgiev
  • Eric Séré

DOI: 10.1007/BF01254347

Cite this article as:
Esteban, M.J., Georgiev, V. & Séré, E. Calc. Var (1996) 4: 265. doi:10.1007/BF01254347


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.

Mathematics subject classification


Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Maria J. Esteban
    • 1
  • Vladimir Georgiev
    • 2
  • Eric Séré
    • 3
  1. 1.CEREMADE, URA CNRS 749, Université Paris DauphineParis Cedex 16France
  2. 2.Institute of MathematicsBulgarian Academy of SciencesSofiaBulgaria
  3. 3.Courant Institute of Mathematical SciencesNew YorkUSA