Partially coherent solitons of variable shape in a slow Kerr-like medium: Exact solutions

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].