Title: One dimensional Bose-Einstein condensate under the effect of the extended uncertainty principle

Abstract: In this study, an analytical investigation was conducted to assess the effects of the extended uncertainty principle (EUP) on a Bose-Einstein condensate (BEC) described by the deformed one-dimensional Gross-Pitaevskii equation. Analytical and variational solutions were derived for both null and harmonic potentials. Subsequently, we analyzed the probability density and the uncertainty of the position as functions of the deformation parameter $\alpha$. Our findings reveal that the EUP significantly impacts the amplitude and uncertainty position of the bright and dark soliton solutions.