Fourth-order compact scheme for the one-dimensional sine-Gordon equation

2009 ◽  
Vol 25 (3) ◽  
pp. 685-711 ◽  
Author(s):  
Mingrong Cui
Keyword(s):  
Fourth Order ◽  
Gordon Equation ◽  
Compact Scheme ◽  
Sine Gordon Equation ◽  
One Dimensional ◽  
Fourth Order Compact Scheme ◽  
The One

scholarly journals Parametrically Driven One-Dimensional Sine-Gordon Equation and Chaos

1988 ◽  
Vol 43 (8-9) ◽  
pp. 727-733
Author(s):  
B. M. Herbst ◽  
W.-H. Steeb
Keyword(s):  
Driving Force ◽  
Gordon Equation ◽  
Zero Mode ◽  
Space Structure ◽  
Chaotic Behaviour ◽  
Force Frequency ◽  
Sine Gordon Equation ◽  
Mode Structure ◽  
One Dimensional ◽  
The One

AbstractThe chaotic behaviour of the parametrically driven one-dimensional sine-Gordon equation with periodic boundary conditions is studied. The initial condition is u(x, 0) = ƒ(x), ut (x, 0) = 0 where ƒ is the breather solution of the one-dimensional sine-Gordon equation at t = 0. We vary the amplitude of the driving force, the frequency of the driving force and the damping constant. For appropriate values of the driving force, frequency and damping constant chaotic behaviour with respect to the time-evolution of w(x = fixed, t) can be found. The space structure u(t = fixed, x) changes with increasing driving force from a zero mode structure to a breather-like structure consisting of a few modes.

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