  We develop a spatiotemporal mode decomposition technique to study the mode
power distribution of ultrashort pulses emerging from long spans of
graded-index multimode fiber, for different input laser conditions. We find
that beam mode power content in the dispersive pulse propagation regime can be
described by the Bose-Einstein law, as a result of the process of power
diffusion from linear and nonlinear mode coupling among nondegenerate mode
groups. In the soliton regime, the output mode power distribution approaches
the Rayleigh-Jeans law
