Collisions of two solitons in an arbitrary number of coupled nonlinear Schrödinger equations

We show that pairwise soliton collisions in N > 2 intensity-coupled non linear Schr¨odinger equations can be reduced to pairwise soliton collisions in two coupled equations. The reduction applies to a wide class of systems, including N-component Manakov. This greatly simplifies the analysis of such systems and has important implications for the application of soliton collisions to all-optical computing.