2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148634We provide analytical functions approximating $\int e^{-x^2} dx$, the basis of which is the kink soliton and which are both accurate (error $< 0.2 %$) and simple. We demonstrate our results with some applications, particularly to the generation of Gaussian random fields.15 pages, 5 eps figure, Latex2e. To appear in Letters in Applied Mathematics. Significant additions and modificationsCondensed Mattertext