TY - JOUR

T1 - Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein–Gordon equation and numerical comparisons

AU - Muda, Y.

AU - Akbar, F. T.

AU - Kusdiantara, R.

AU - Gunara, B. E.

AU - Susanto, H.

N1 - Funding Information:
YM thanks MoRA ( Ministry of Religious Affairs ) Scholarship of the Republic of Indonesia for a financial support. The research of FTA and BEG is supported by PDUPT Kemenristekdikti 2018. RK gratefully acknowledges financial support from Lembaga Pengelolaan Dana Pendidikan (Indonesian Endowment Fund for Education) (Grant No. – Ref: S-34/LPDP.3/2017 ). The authors are grateful to the four reviewers for their comments that improved the quality of the manuscript.
Funding Information:
YM thanks MoRA (Ministry of Religious Affairs) Scholarship of the Republic of Indonesia for a financial support. The research of FTA and BEG is supported by PDUPT Kemenristekdikti 2018. RK gratefully acknowledges financial support from Lembaga Pengelolaan Dana Pendidikan (Indonesian Endowment Fund for Education) (Grant No. – Ref: S-34/LPDP.3/2017). The authors are grateful to the four reviewers for their comments that improved the quality of the manuscript.
Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2019/4/10

Y1 - 2019/4/10

N2 - We consider a damped, parametrically driven discrete nonlinear Klein–Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of solutions to the discrete nonlinear Schrödinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schrödinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein–Gordon equation.

AB - We consider a damped, parametrically driven discrete nonlinear Klein–Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of solutions to the discrete nonlinear Schrödinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schrödinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein–Gordon equation.

KW - Discrete breather

KW - Discrete Klein–Gordon equation

KW - Discrete nonlinear Schrödinger equation

KW - Discrete soliton

KW - Small-amplitude approximation

UR - http://www.scopus.com/inward/record.url?scp=85060858874&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2019.01.047

DO - 10.1016/j.physleta.2019.01.047

M3 - Article

AN - SCOPUS:85060858874

SN - 0375-9601

VL - 383

SP - 1274

EP - 1282

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 12

ER -