Numerical simulation of quasi-periodic solutions of the sine-Gordon equation

1995 ◽  
Vol 87 (1-4) ◽  
pp. 37-47 ◽  
Author(s):  
Mark J. Ablowitz ◽  
B.M. Herbst ◽  
Constance M. Schober
Keyword(s):  
Numerical Simulation ◽  
Periodic Solutions ◽  
Gordon Equation ◽  
Sine Gordon Equation

Quasi-periodic solutions of the sine-Gordon equation

1982 ◽  
Vol 92 (9) ◽  
pp. 427-430 ◽  
Author(s):  
M. Jaworski ◽  
J. Zagrodziński
Keyword(s):  
Periodic Solutions ◽  
Gordon Equation ◽  
Sine Gordon Equation

scholarly journals Interaction of Solitons for Sine-Gordon-Type Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Georgii A. Omel’yanov ◽  
Israel Segundo-Caballero
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Analysis ◽  
Small Parameter ◽  
Wave Equations ◽  
Gordon Equation ◽  
Sine Gordon Equation ◽  
Semilinear Wave Equations ◽  
The Subject ◽  
Interaction Of Solitons

The subject of our consideration is a family of semilinear wave equations with a small parameter and nonlinearities which provide the existence of kink-type solutions (solitons). Using asymptotic analysis and numerical simulation, we demonstrate that solitons of the same type (kinks or antikinks) interact in the same manner as for the sine-Gordon equation. However, solitons of the different type preserve the shape after the interaction only in the case of two or three waves, and, moreover, under some additional conditions.

scholarly journals Exact Traveling Wave Solutions for the Modified Double Sine-Gordon Equation

2015 ◽  
Vol 7 (2) ◽  
pp. 182
Author(s):  
Ying Huang ◽  
Bao Rong Li
Keyword(s):  
Periodic Solutions ◽  
Traveling Wave ◽  
Gordon Equation ◽  
Traveling Wave Solutions ◽  
Sine Gordon Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Different Types ◽  
Elementary Methods ◽  
Sg Equation

With some elementary  methods, a number of new travelling  solutions of  the  modified double Sine-Gordon (SG) equation are obtained,including different types of exact solion solutions and exact periodic solutions.

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