  Experimental and numerical studies of spatiotemporal femtosecond soliton
propagation over up to 1 km spans of parabolic graded-index (GRIN) fibers
reveal that initial multimode soliton pulses naturally and irreversibly evolve
into a singlemode soliton. This is carried by the fundamental mode of the
fiber, which acts as a dynamical attractor of the multimode system for up to
the record value (for multimode fibers) of 5600 chromatic dispersion distances.
This experimental evidence invalidates the use of variational approaches, which
intrinsically require that the initial multimode propagation of a self-imaging
soliton is indefinitely maintained.
