  We report the existence of transversely stable soliton trains in optics.
These stable soliton trains are found in two-dimensional square photonic
lattices when they bifurcate from X-symmetry points with saddle-shaped
diffraction inside the first Bloch band and their amplitudes are above a
certain threshold. We also show that soliton trains with low amplitudes or
bifurcated from edges of the first Bloch band (Gamma and M points) still suffer
transverse instability. These results are obtained in the continuous lattice
model and further corroborated by the discrete model.
