Symmetry analysis of the nonlinear two-dimensional Klein-Gordon equation with a time-varying delay

2017 ◽  
Author(s):  
Feng-Shan Long ◽  
S. V. Meleshko
Keyword(s):  
Gordon Equation ◽  
Symmetry Analysis ◽  
Time Varying ◽  
Two Dimensional ◽  
Time Varying Delay ◽  
Klein Gordon ◽  
Varying Delay ◽  
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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