  We examine spatial localisation and dynamical stability of Bose-Einstein
condensates of exciton-polaritons in microcavities under the condition of
off-resonant spatially inhomogeneous optical pumping both with and without a
harmonic trapping potential. We employ the open-dissipative Gross-Pitaevskii
model for describing an incoherently pumped polariton condensate coupled to an
exciton reservoir, and reveal that spatial localisation of the steady-state
condensate occurs due to the effective self-trapping created by the polariton
flows supported by the spatially inhomogeneous pump, regardless of the presence
of the external potential. A ground state of the polariton condensate with
repulsive interactions between the quasiparticles represents a dynamically
stable bright dissipative soliton. We also investigate the conditions for
sustaining spatially localised structures with non-zero angular momentum in the
form of single-charge vortices.
