scholarly journals Orbital stability of periodic standing waves for the logarithmic Klein-Gordon equation

2020 ◽  
Vol 484 (2) ◽  
pp. 123723
Author(s):  
Fábio Natali ◽  
Eleomar Cardoso
Keyword(s):  
Gordon Equation ◽  
Standing Waves ◽  
Orbital Stability ◽  
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 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.

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 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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