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

Maria J. Esteban, Vladimir Simeonov Gueorguiev, Eric Séré

Research output: Contribution to journalArticle

72 Citations (Scopus)

Abstract

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
Volume4
Issue number3
Publication statusPublished - 1996 Apr
Externally publishedYes

Fingerprint

Klein-Gordon Equation
Dirac Equation
Stationary Solutions
Solitons
Paul Adrien Maurice Dirac
Soliton-like Solutions
Electromagnetic fields
Energy Functional
Variational Methods
Electromagnetic Fields
Compactness
Electrons
Critical point
Space-time
Electron
Interaction
Model

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations. / Esteban, Maria J.; Gueorguiev, Vladimir Simeonov; Séré, Eric.

In: Calculus of Variations and Partial Differential Equations, Vol. 4, No. 3, 04.1996, p. 265-281.

Research output: Contribution to journalArticle

@article{0d47acacf35d442384b03aa7e99aa3f9,
title = "Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations",
abstract = "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.",
author = "Esteban, {Maria J.} and Gueorguiev, {Vladimir Simeonov} and Eric S{\'e}r{\'e}",
year = "1996",
month = "4",
language = "English",
volume = "4",
pages = "265--281",
journal = "Calculus of Variations and Partial Differential Equations",
issn = "0944-2669",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations

AU - Esteban, Maria J.

AU - Gueorguiev, Vladimir Simeonov

AU - Séré, Eric

PY - 1996/4

Y1 - 1996/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=3042986444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042986444&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:3042986444

VL - 4

SP - 265

EP - 281

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

IS - 3

ER -