Multiple normalized standing-wave solutions to the scalar non-linear Klein-Gordon equation with two competing powers

2020 ◽  
Vol 269 (11) ◽  
pp. 9189-9223
Author(s):  
Daniele Garrisi
Keyword(s):  
Standing Wave ◽  
Gordon Equation ◽  
Wave Solutions ◽  
Non Linear ◽  
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.

A Bohmian approach to the perturbations of non-linear Klein–Gordon equation

Pramana ◽  
2016 ◽  
Vol 87 (2) ◽  
Author(s):  
FARAMARZ RAHMANI ◽  
MEHDI GOLSHANI ◽  
MOHSEN SARBISHEI
Keyword(s):  
Gordon Equation ◽  
Non Linear ◽  
Klein Gordon ◽  
Klein Gordon Equation

Weakly non-linear, slowly varying waves and their instabilities

1972 ◽  
Vol 72 (1) ◽  
pp. 95-104 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Variational Principle ◽  
Gordon Equation ◽  
Transport Equations ◽  
Linear Wave ◽  
Leading Order ◽  
Non Linear ◽  
Klein Gordon ◽  
Wave Trains ◽  
Klein Gordon Equation

AbstractA non-linear Klein–Gordon equation is used to discuss the theory of slowly varying, weakly non-linear wave trains. An averaged variational principle is used to obtain transport equations for the slow variations which incorporate the leading order modulation and non-linear terms. Linearized transport equations are used to discuss instabilities.

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