Bose–Einstein condensate crossover regime. Starting from the extended Thomas–Fermi
density functional theory of superfluid order parameter, a density transformation is used to
map the hydrodynamic mean field equation to a Lienard-type equation. As a result, bell
solitons are obtained as exact solutions, which is further verified by the numerical solution of
the dynamical equation. The stability of the soliton is established and its behaviour in the …