  Solitons, nonlinear particle-like excitations with inalterable properties
(amplitude, shape, and velocity) as they propagate, are omnipresent in many
branches of science---and in physics in particular. Flat-top solitons are a
novel type of bright solitons that have not been well explored in pure
nonlinear media. Here, a model of nonlinear Kerr (cubic) media of ultracold
atoms with spatially modulated repulsive interactions is proposed and shown to
support a vast variety of stable flat-top matter-wave solitons, including
one-dimensional (1D) flat-top fundamental and multipole solitons,
two-dimensional (2D) flat-top fundamental and vortex solitons. We demonstrate
that by varying the relevant physical parameters (nonlinearity coefficient and
chemical potential) the ordinary bright (gaussian) solitons can transform into
the novel flat-top solitons. The (in-)stability domains of the flat-top soliton
families are checked by means of linear stability analysis and reconfirmed by
direct numerical simulations. This model is generic in the contexts of
nonlinear optics and Bose-Einstein condensates, which provide direct
experimental access to observe the predicted solutions.

Pattern Formation and Solitons;Quantum Gases;Optics