We carry out a theoretical investigation of the properties of partially coh
erent solitons for media which have a slow Kerr-like nonlinearity. We find
exact solutions of the Nth-order Manakov equations in a general form. These
describe partially coherent solitons (PCSs) and their collisions. In fact,
the exact solutions allow us to analyze important properties of PCSs such
as stationary profiles oft the spatial beams and effects resulting from the
ir collisions. In particular, we find, analytically, the number of paramete
rs that control the soliton shape. We present profiles which are symmetric
as well as those which are asymmetric. We also find that collisions allow t
he profiles to remain stationary but cause their shapes to change. [S1063-6
51X(99)08705-X].