Solution of non-linear Klein–Gordon equation with a quadratic non-linear term by Adomian decomposition method

2009 ◽  
Vol 14 (3) ◽  
pp. 718-723 ◽  
Author(s):  
Kartik Chandra Basak ◽  
Pratap Chandra Ray ◽  
Rasajit Kumar Bera
Keyword(s):  
Decomposition Method ◽  
Gordon Equation ◽  
Adomian Decomposition Method ◽  
Linear Term ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Klein Gordon ◽  
Klein Gordon Equation

Numerical Solution of Time-Fractional Klein–Gordon Equation by Using the Decomposition Methods

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hossein Jafari
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Gordon Equation ◽  
Adomian Decomposition Method ◽  
Type Equation ◽  
Decomposition Methods ◽  
Adomian Decomposition ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. We compare these methods and discuss the convergence of them. The obtained results reveal that these methods are very accurate and effective.

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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