We develop a theory of modulational instability of multiparameter solitary
waves and analyze the transverse instability of composite (or vector) optic
al solitons in a saturable nonlinear medium. We demonstrate theoretically a
nd experimentally that a soliton stripe breaks up into an array of (2+1)-di
mensional dipole-mode vector solitons, thus confirming the robust nature of
those solitons as fundamental composite structures of incoherently coupled
fields.