Modeling Solitonic Cores, Stabilization of Bar, and Suppression of Bar Dissolution in DDO 168 via GPP Formalism: A Detailed Analysis of Bose–Einstein Condensate/Fuzzy Dark Matter Halo Structure and Bar Dynamics in the Dwarf Galaxy DDO 168

Abstract The cusp–core problem remains a challenge to the ΛCDM model, since dwarf galaxies often exhibit flat central density cores rather than the steep cusps ( ρ ∝ r −1 ) predicted by collisionless N -body simulations. We model the dark-matter-dominated dwarf irregular galaxy DDO 168 within the Bose–Einstein condensate (BEC) or fuzzy dark matter (FDM) framework, in which ultralight bosons form a solitonic core governed by the Gross–Pitaevskii–Poisson (GPP) equations, with the soliton mass–radius relation enforced. We numerically validate the ground-state solution of the GPP system as a consistency check and fit the inner rotation curve of DDO 168 using SPARC data. Within this framework, the data are consistent with an axion mass m = ( 1 . 3 − 0.2 + 0.3 ) × 1 0 − 23 eV , and yield a solitonic core with characteristic radius R c = 2.4 0 − 0.24 + 0.22 kpc , enclosing a mass M (