Nonlinear propagation in multi-mode fibers in the strong coupling regime

We show that light propagation in a group of degenerate modes of a multi-mode optical fiber in the presence of random mode coupling is described by a multi-component Manakov equation, thereby making multi-mode fibers the first reported physical system that admits true multi-component soliton solutions. The nonlinearity coefficient appearing in the equation is expressed rigorously in terms of the multi-mode fiber parameters.