A sixth-order nonlinear Schrödinger equation as a reduction of the nonlinear Klein–Gordon equation for slowly modulated wave trains

2018 ◽  
Vol 94 (3) ◽  
pp. 1921-1932 ◽  
Author(s):  
Yuri V. Sedletsky ◽  
Ivan S. Gandzha
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Gordon Equation ◽  
Nonlinear Schrodinger Equation ◽  
Sixth Order ◽  
Klein Gordon ◽  
Wave Trains ◽  
Modulated Wave Trains ◽  
Klein Gordon Equation

scholarly journals Reduction of a damped, driven Klein–Gordon equation into a discrete nonlinear Schrödinger equation: Justification and numerical comparison

2020 ◽  
Vol 120 (1-2) ◽  
pp. 73-86 ◽  
Author(s):  
Yuslenita Muda ◽  
Fiki T. Akbar ◽  
Rudy Kusdiantara ◽  
Bobby E. Gunara ◽  
Hadi Susanto
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Gordon Equation ◽  
Nonlinear Schrodinger Equation ◽  
Numerical Comparison ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Nonlinear Schrödinger ◽  
Klein Gordon ◽  
Klein Gordon Equation

We consider a discrete nonlinear Klein–Gordon equation with damping and external drive. Using a small amplitude ansatz, one usually approximates the equation using a damped, driven discrete nonlinear Schrödinger equation. Here, we show for the first time the justification of this approximation by finding the error bound using energy estimate. Additionally, we prove the local and global existence of the Schrödinger equation. Numerical simulations are performed that describe the analytical results. Comparisons between discrete breathers of the Klein–Gordon equation and discrete solitons of the discrete nonlinear Schrödinger equation are presented.

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