  We present a variety of dissipative solitons and breathing modes in a medium
with localized gain and homogeneous linear dissipation. The system posses a
number of unusual properties, like exponentially localized modes in both
focusing and defocusing media, the existence of modes in focusing media at
negative propagation constant values, the simultaneous existence of stable
symmetric and anti-symmetric localized modes when the gain landscape possesses
two local maxima, as well as the existence of stable breathing solutions.
