Eliminating The Transverse Instabilities Of Kerr Solitons

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.