  In spite of the massive interest that the generalized Manakov equation has
attracted in the past two decades, no physical system which is quantitatively
described by this equation has been reported so far. In this paper we show that
propagation in a group of degenerate modes of a multi-mode optical fiber
satisfies this equation in the presence of random mode coupling. Consequently,
this is the first reported physical system that admits true multi-component
soliton solutions. The reported formalism constitutes the starting point for
future studies of nonlinear effects in multi-mode fiber transmission.
