scholarly journals Solitary wave of ground state type for a nonlinear Klein–Gordon equation coupled with Born–Infeld theory in ℝ2

2020 ◽  
pp. 1-18
Author(s):  
Francisco Albuquerque ◽  
Shang-Jie Chen ◽  
Lin Li
Keyword(s):  
Solitary Wave ◽  
Ground State ◽  
Gordon Equation ◽  
State Type ◽  
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.

Bound state solutions of the hyper-radial Klein-Gordon equation under the Deng-Fan potential by WKB and SWKB method

2021 ◽  
Author(s):  
Ekwevugbe Omugbe ◽  
Omosede Eromwon Osafile ◽  
Etido P. Inyang ◽  
Arezu Jahanshir
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Gordon Equation ◽  
Energy Levels ◽  
Bound State ◽  
Ground State Wave Function ◽  
Wkb Approximation ◽  
Energy Spectra ◽  
Klein Gordon ◽  
Klein Gordon Equation

Abstract The energy levels of the Klein-Gordon equation in hyper-radial space under the Deng-Fan potential energy function are studied by the SWKB and WKB approximation methods. We obtained the analytic solution of the energy spectra and the ground state wave function in closed form. Furthermore, we obtained the energy equation corresponding to the Schrodinger equation by invoking the non-relativistic limit. The variations of the non-relativistic N-dimensional energy spectra with the potential parameters and radial quantum number are investigated. The energy levels are degenerate for N= 2, N=4 and increase with the dimensionality number. The ground state wave function and its gradient are continuous at the boundary r=0,r=∞. Our results for the energy spectra are in excellent agreement with the ones obtained by other analytical methods where similar centrifugal approximations were applied. We show that the semi-classical methods notably the SWKB and WKB approximation still offer an effective and the simplest approach for solving the bound state problems in theoretical physics.

On the Orbital Stability of Standing-Wave Solutions to a Coupled Non-Linear Klein-Gordon Equation

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Daniele Garrisi
Keyword(s):  
Standing Wave ◽  
Ground State ◽  
Gordon Equation ◽  
Standing Waves ◽  
Orbital Stability ◽  
Wave Solutions ◽  
Non Linear ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractWe show the existence of standing-wave solutions to a coupled non-linear Klein-Gordon equation. Our solutions are obtained as minimizers of the energy under a two-charges constraint. We prove that the ground state is stable and that standing-waves are orbitally stable under a non-degeneracy assumption.

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