Direct meshless local Petrov–Galerkin method for the two-dimensional Klein–Gordon equation

2017 ◽  
Vol 74 ◽  
pp. 1-13 ◽  
Author(s):  
Mohammadreza Ahmadi Darani
Keyword(s):  
Galerkin Method ◽  
Gordon Equation ◽  
Two Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation

A method for generating exact solutions of the nonlinear Klein–Gordon equation

1992 ◽  
Vol 70 (6) ◽  
pp. 467-469 ◽  
Author(s):  
A. Grigorov ◽  
N. Martinov ◽  
D. Ouroushev ◽  
Vl. Georgiev
Keyword(s):  
Electromagnetic Field ◽  
Phase Velocity ◽  
Exact Solutions ◽  
Gordon Equation ◽  
External Electromagnetic Field ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Simple Method ◽  
Klein Gordon ◽  
Klein Gordon Equation

A simple method for generating the exact solutions of the nonlinear Klein–Gordon equation is proposed. The solutions obtained depend on two arbitrary functions and are in the form of running waves. An application of one of the solutions for the (2 + 1) – dimensional sine-Gordon equation is proposed. It concerns the selective properties of a two-dimensional semi-infinite Josephson junction with regard to an external electromagnetic field in the form of running waves with a phase velocity equal to the Swihart velocity. A method for measuring the Swihart velocity is presented.

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