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 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

Mechanics of a charged particle on the Kaluza–Klein background

1995 ◽  
Vol 73 (9-10) ◽  
pp. 602-607 ◽  
Author(s):  
S. R. Vatsya
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Integral Method ◽  
Gordon Equation ◽  
Type Equation ◽  
Fifth Dimension ◽  
Klein Gordon ◽  
Path Integral Method ◽  
Klein Gordon Equation ◽  
Kaluza Klein

The path-integral method is used to derive a generalized Schrödinger-type equation from the Kaluza–Klein Lagrangian for a charged particle in an electromagnetic field. The compactness of the fifth dimension and the properties of the physical paths are used to decompose this equation into its infinite components, one of them being similar to the Klein–Gordon equation.

Electromagnetic interaction with the Klein–Gordon equation in the framework of GUP

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
B. Khosropour
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Uncertainty Principle ◽  
Electric Potential ◽  
Uniform Magnetic Field ◽  
Gordon Equation ◽  
Electromagnetic Interaction ◽  
Generalized Uncertainty Principle ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this work, according to the generalized uncertainty principle, we study the Klein–Gordon equation interacting with the electromagnetic field. The generalized Klein–Gordon equation is obtained in the presence of a scalar electric potential and a uniform magnetic field. Furthermore, we find the relation of the generalized energy–momentum in the presence of a scalar electric potential and a uniform magnetic field separately.

scholarly journals Non-Existence Results for the Coupled Klein-Gordon-Maxwell Equations

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Teresa D’Aprile ◽  
Dimitri Mugnai
Keyword(s):  
Electrostatic Field ◽  
Maxwell Equations ◽  
Gordon Equation ◽  
Necessary Conditions ◽  
Existence Results ◽  
Pohozaev Identity ◽  
Nontrivial Solutions ◽  
Coupled Equations ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractIn this paper we obtain some non-existence results for the Klein-Gordon equation coupled with the electrostatic field. The method relies on the deduction of some suitable Pohožaev identity which provides necessary conditions to get existence of nontrivial solutions. The case of Maxwell-Schrödinger type coupled equations is also considered.

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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