Reduction of damped, driven Klein-Gordon equations into a discrete nonlinear Schrödinger equation: justification and numerical comparisons

2019/11/05 by Yuslenita Muda, Fiki T. Akbar, Rudy Kusdiantara +2 · 2 citations
Physics and Astronomy · Mathematics · #nlin.PS #math-ph #math.MP

paper · pdf · doi:10.3233/asy-191579

published as Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-14, 2019

arxiv created 2019/11/05 · arxiv updated 2019/11/06

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 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.

Cited by

• Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons
• Supratransmission of rogue wave-like breathing solitons

Related

• Global existence in infinite lattices of nonlinear oscillators: The Discrete Klein-Gordon equation
• Well-posedness of the discrete nonlinear Schrödinger equations and the Klein-Gordon equations
• Existence, linear stability and long-time nonlinear stability of Klein-Gordon breathers in the small-amplitude limit
• Justification of the Nonlinear Schrödinger approximation for a quasilinear Klein-Gordon equation
• Solitons in a modified discrete nonlinear Schroedinger equation