Existence and non-existence of solitary waves for the critical Klein–Gordon equation coupled with Maxwell's equations

2004 ◽  
Vol 58 (7-8) ◽  
pp. 733-747 ◽  
Author(s):  
D CASSANI
Keyword(s):  
Solitary Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals The Helmholtzian Operator and Maxwell-Cassano Equations of an Electromagnetic-nuclear Field

2019 ◽  
pp. 8-12
Author(s):  
Claude Michael Cassano
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Nuclear Field ◽  
Klein Gordon ◽  
Klein Gordon Equation

This article demonstrates that when acting on a four-vector doublet, the Helmholtzian may be factored into two 4×4/8×8 differential matrices, resulting in a four-vector doublet Klein-Gordon equation with source. This factorization enables yielding of a mass-generalized set of Maxwell’s equations.

scholarly journals Finsler geometry as a model for relativistic gravity

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1850166 ◽  
Author(s):  
Claus Lämmerzahl ◽  
Volker Perlick
Keyword(s):  
General Relativity ◽  
Dirac Equation ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Finsler Geometry ◽  
Experimental Tests ◽  
The Status ◽  
Klein Gordon ◽  
Klein Gordon Equation

We give an overview on the status and on the perspectives of Finsler gravity, beginning with a discussion of various motivations for considering a Finslerian modification of General Relativity. The subjects covered include Finslerian versions of Maxwell’s equations, of the Klein–Gordon equation and of the Dirac equation, and several experimental tests of Finsler gravity.

Relativistic Wave Equations

2019 ◽  
pp. 25-42
Author(s):  
Michael E. Peskin
Keyword(s):  
Dirac Equation ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Relativistic Wave Equations ◽  
Quantum Mechanical ◽  
Relativistic Wave ◽  
Klein Gordon ◽  
Klein Gordon Equation

This chapter presents the wave equations that govern the behavior of quantum mechanical particles with spin 0, 1/2, and 1 in relativistic theories. These equations are the Klein-Gordon equation, the Dirac equation, and Maxwell’s equations.

scholarly journals Multi-Solitary Waves for the Nonlinear Klein-Gordon Equation

2014 ◽  
Vol 39 (8) ◽  
pp. 1479-1522 ◽  
Author(s):  
Jacopo Bellazzini ◽  
Marco Ghimenti ◽  
Stefan Le Coz
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS

2002 ◽  
Vol 14 (04) ◽  
pp. 409-420 ◽  
Author(s):  
VIERI BENCI ◽  
DONATO FORTUNATO FORTUNATO
Keyword(s):  
Electromagnetic Field ◽  
Solitary Wave ◽  
Electric Field ◽  
Solitary Waves ◽  
Maxwell Equations ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

This paper is divided in two parts. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. In the second part we study the electrostatic case. We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ.

scholarly journals Solitons for the Nonlinear Klein-Gordon Equation

2010 ◽  
Vol 10 (2) ◽  
Author(s):  
J. Bellazzini ◽  
V. Benci ◽  
C. Bonanno ◽  
A.M. Micheletti
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Energy Charge ◽  
Sufficient Conditions ◽  
Orbital Stability ◽  
Field Equations ◽  
Klein Gordon ◽  
Ratio Energy ◽  
Klein Gordon Equation

AbstractIn this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the ratio energy/charge of a function, which turns out to be a useful approach for many field equations.

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