  We address the existence and stability of spatial localized modes supported
by a parity-time-symmetric complex potential in the presence of power-law
nonlinearity. The analytical expressions of the localized modes, which are
Gaussian in nature, are obtained in both (1+1) and (2+1) dimensions. A linear
stability analysis corroborated by the direct numerical simulations reveals
that these analytical localized modes can propagate stably for a wide range of
the potential parameters and for various order nonlinearities. Some dynamical
characteristics of these solutions, such as the power and the transverse
power-flow density, are also examined.
