2025-08-262025-08-262025COUTO, Hugo L. C.; AVELAR, Ardiley T.; CARDOSO, Wesley B. Effective 1D-equation with a Lambert W function nonlinearity for cigar-shaped Bose-Einstein condensates. Communications in Nonlinear Science and Numerical Simulation, Amsterdam, v. 140, pt. 2, e108447, 2025. DOI: https://doi.org/10.1016/j.cnsns.2024.108447. Disponível em: https://www.sciencedirect.com/science/article/pii/S1007570424006324. Acesso em: 25 ago. 2025.1007-5704e- 1878-7274https://www.sciencedirect.com/science/article/pii/S1007570424006324In this paper, we derive an effective 1D equation based on the work of Mateo and Delgado [Phys. Rev. A 77, 013617 (2008)] that governs the axial dynamics of mean-field cigar-shaped Bose–Einstein condensates (BECs) with repulsive interatomic interactions and subject to transverse anti-Gaussian confining potential. The resulting equation exhibits a nonstandard nonlinearity written in terms of the principal branch of the Lambert W function. This equation appropriately encompasses the correct limits within the Thomas–Fermi (TF) and perturbative regimes. The validity of our findings was established through a comparative analysis with numerical solutions derived from the complete three-dimensional Gross–Pitaevskii equation, including those about the limiting cases encountered in the TF and perturbative regimes.engAcesso RestritoBose–Einstein condensateEffective equationsAnti-Gaussian potentialLambert W functionArtigohttps://doi.org/10.1016/j.cnsns.2024.108447