Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schr\"{o}dinger lattices
Pattern Formation and Solitons
2018-11-16 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1811.06480,
title = {Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schr\"{o}dinger lattices},
author = {Rahmi Rusin and Rudy Kusdiantara and Hadi Susanto},
journal= {arXiv preprint arXiv:1811.06480},
year = {2018}
}