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Reduction of a damped, driven Klein–Gordon equation into a discrete nonlinear Schrödinger equation: Justification and numerical comparison
We consider a discrete nonlinear Klein-Gordon equations 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. …