We study a generalised Gross–Pitaevskii equation describing a d-dimensional harmonic trapped (with trap frequency ω 0) weakly interacting Bose gas with a nonlinearity 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.