Reduction of damped, driven Klein-Gordon equations into a discrete nonlinear Schr\"odinger equation: justification and numerical comparisons
Pattern Formation and Solitons
2019-11-06 v1 Mathematical Physics
math.MP
Abstract
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 Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger equation are presented.
Keywords
Cite
@article{arxiv.1911.01631,
title = {Reduction of damped, driven Klein-Gordon equations into a discrete nonlinear Schr\"odinger equation: justification and numerical comparisons},
author = {Yuslenita Muda and Fiki T. Akbar and Rudy Kusdiantara and Bobby E. Gunara and Hadi Susanto},
journal= {arXiv preprint arXiv:1911.01631},
year = {2019}
}