Strong Instability of Standing Waves for the Nonlinear Klein–Gordon Equation and the Klein–Gordon–Zakharov System

2007 ◽  
Vol 38 (6) ◽  
pp. 1912-1931 ◽  
Author(s):  
Masahito Ohta ◽  
Grozdena Todorova
Keyword(s):  
Gordon Equation ◽  
Standing Waves ◽  
Zakharov System ◽  
Strong Instability ◽  
Klein Gordon ◽  
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 From the Klein-Gordon-Zakharov system to the Klein-Gordon equation

2016 ◽  
Vol 39 (18) ◽  
pp. 5371-5380 ◽  
Author(s):  
Markus Daub ◽  
Guido Schneider ◽  
Katharina Schratz
Keyword(s):  
Gordon Equation ◽  
Zakharov System ◽  
Klein Gordon ◽  
Klein Gordon Equation

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.

scholarly journals Fractional Klein-Gordon equation with singular mass

2021 ◽  
Vol 143 ◽  
pp. 110579
Author(s):  
Arshyn Altybay ◽  
Michael Ruzhansky ◽  
Mohammed Elamine Sebih ◽  
Niyaz Tokmagambetov
Keyword(s):  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation
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