The large-scale expansion dynamics of quantum gases is a central tool in ultracold gas experiments and poses great challenges to theory.
In this work, we provide an accurate reformulation of the Gross-Pitaevskii equation for ultracold Bose gases in a coordinate frame that scales adaptively with the system size during evolution, with long evolution times during expansion or similar large-scale operations. allows the simulation of Our approach does not make hydrodynamic approximations, is not restricted to scaling hypotheses, harmonic potentials or energy eigenstates, and can be easily generalized to non-contact interactions via appropriate stress tensors of quantum fluids . Applications include simulating ideal gas expansions, cigar-shaped condensates in the Thomas-Fermi regime, and linear superpositions of counter-propagating Gaussian wavepackets. We recover the known scaling of the ideal gas and Thomas-Fermi regime and identify a linear regime of aspect ratios that maintains free expansion. Analysis of the scaling dynamics equation shows that exact aspect-ratio-invariant free expansion does not exist in nonlinear evolution. Our treatment allows investigation of nonlinear effects in matter wave dynamics in large-scale changing evolution.