Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schr\"{o}dinger lattices

Rahmi Rusin et al 2018 J. Phys. A: Math. Theor. 51 475202 We study the fundamental lattice solitons of the discrete nonlinear Schr\"{o}dinger (DNLS) equation and their stability via a variational method. Using a Gaussian ansatz and comparing the results with numerical computations, we report a...

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Bibliographic Details
Main Authors Rusin, Rahmi, Kusdiantara, Rudy, Susanto, Hadi
Format Journal Article
LanguageEnglish
Published 15.11.2018
Subjects
Physics - Pattern Formation and Solitons
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Summary:Rahmi Rusin et al 2018 J. Phys. A: Math. Theor. 51 475202 We study the fundamental lattice solitons of the discrete nonlinear Schr\"{o}dinger (DNLS) equation and their stability via a variational method. Using a Gaussian ansatz and comparing the results with numerical computations, we report a novel observation of false instabilities. Comparing with established results and using Vakhitov-Kolokolov criterion, we deduce that the instabilities are due to the ansatz. In the context of using the same type of ansatzs, we provide a remedy by employing multiple Gaussian functions. The results show that the higher the number of Gaussian function used, the better the solution approximation.
DOI:10.48550/arxiv.1811.06480