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arXiv · 1811.06480

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

Rahmi Rusin·Rudy Kusdiantara·Hadi Susanto
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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.

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Rahmi Rusin, Rudy Kusdiantara, Hadi Susanto. 2018-11-15. Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schr\"{o}dinger lattices. https://doi.org/10.1088/1751-8121%2Faae4be

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