Variational approximations using Gaussian ansatz, false instability, and its remedy in nonlinear Schrödinger lattices

Abstract

We study the fundamental lattice solitons of the discrete nonlinear Schrödinger (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.