Linear Stability Analysis for Periodic Standing Waves of the Klein–Gordon Equation

2013 ◽  
Vol 22 (2) ◽  
pp. 209-219
Author(s):  
Sevdzhan Hakkaev
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Gordon Equation ◽  
Standing Waves ◽  
Klein Gordon ◽  
Periodic Standing Waves ◽  
Klein Gordon Equation

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.

scholarly journals Stability of standing waves for a nonlinear Klein–Gordon equation with delta potentials

2019 ◽  
Vol 268 (1) ◽  
pp. 353-388
Author(s):  
Elek Csobo ◽  
François Genoud ◽  
Masahito Ohta ◽  
Julien Royer
Keyword(s):  
Gordon Equation ◽  
Standing Waves ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Linear stability of Mandal–Sengupta–Wadia black holes

2019 ◽  
Vol 34 (12) ◽  
pp. 1950094
Author(s):  
H. Gürsel ◽  
G. Tokgöz ◽  
İ. Sakallı
Keyword(s):  
Black Holes ◽  
Linear Stability ◽  
Gordon Equation ◽  
Small Time ◽  
Einstein Equations ◽  
Time Dependent ◽  
Small Perturbations ◽  
Klein Gordon ◽  
Dimensional Gravity ◽  
Klein Gordon Equation

In this paper, the linear stability of static Mandal–Sengupta–Wadia (MSW) black holes in (2 + 1)-dimensional gravity against circularly symmetric perturbations is studied. Our analysis only applies to non-extremal configurations, thus leaving out the case of the extremal (2 + 1) MSW solution. The associated fields are assumed to have small perturbations in these static backgrounds. We then consider the dilaton equation and specific components of the linearized Einstein equations. The resulting effective Klein–Gordon equation is reduced to the Schrödinger-like wave equation with the associated effective potential. Finally, it is shown that MSW black holes are stable against the small time-dependent perturbations.

scholarly journals Semiclassical Limit For the Nonlinear Klein Gordon Equation in Bounded Domains

2009 ◽  
Vol 9 (1) ◽  
Author(s):  
Marco G. Ghimenti ◽  
Carlo R. Grisanti
Keyword(s):  
Critical Point ◽  
Gordon Equation ◽  
Semiclassical Limit ◽  
Standing Waves ◽  
Stationary Solutions ◽  
Point Problem ◽  
Bounded Domains ◽  
Variational Techniques ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractWe are interested in the existence of standing waves for the nonlinear Klein Gordon equation εWe want to use a Benci-Cerami type argument in order to prove a the existence of several standing waves localized in suitable points of D. The main result of this paper is that, under suitable growth condition on W, for ε suffciently small, we have at least cat(D) stationary solutions of equation (†), where cat(D) is the Ljusternik-Schnirelmann category. The proof is achieved by solving a constrained critical point problem via variational techniques.

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