  We show analytically, numerically, and experimentally that a transversely
stable one-dimensional [(1+1)D] bright Kerr soliton can exist in a 3D bulk
medium. The transverse instability of the soliton is completely eliminated if
it is made sufficiently incoherent along the transverse dimension. We derive a
criterion for the threshold of transverse instability that links the
nonlinearity to the largest transverse correlation distance for which the 1D
soliton is stable
