We consider soliton dynamics and stability in a nonlinear lattice formed by alternating domains with focusing cubic and saturable nonlinearities. We find that in such lattices, solitons centered on cubic domains may be stabilized even in two-dimensional geometries, in spite of their intrinsic catastrophic instability in the absence of the lattice. Solitons centered on saturable domains are always unstable.
Borovkova, O., Kartashov, Y., Torner, L. Stabilization of two-dimensional solitons in cubic-saturable nonlinear lattices. "Physical review A", 4 Juny 2010, vol. 81, núm. 6, p. 1-16.