2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/17128We study a generalised Gross-Pitaevskii equation describing a d-dimensional harmonic trapped (with trap frequency $ω_{0}$) weakly interacting Bose gas with a non-linearity of order (2 k + 1) and scaling exponent (n) of the interaction potential. Using the time-dependent variational analysis, we explicitly show that for a particular combination of n, k and d, the generalised GP equation has the universal monopole oscillation frequency $2 ω_{0}$. We also find that the time-evolution of the width can be described universally by the same Hill's equation if the system satisfy that particular combination. We also obtain the condition for the exact self-similar solutions of the Gross-Pitaevskii equation. As an application, we discuss low dimensional trapped Bose condensate state and Calogero model.7 pages, revtex file, No figures, version to appear in Physics Letters ASoft Condensed MatterStatistical Mechanicstext