We address the existence and stability of two-dimensional solitons in optical or matter-wave media, which are supported by purely nonlinear lattices in the form of a periodic array of cylinders with self-focusing nonlinearity, embedded into a linear material. We show that such lattices can stabilize two-dimensional solitons against collapse. We also found that stable multipoles and vortex solitons are also supported by nonlinear lattices, provided that the nonlinearity exhibits saturation.
Kartashov, Y.V., Malomed, B., Vysloukh, V.A., Torner, L. Two-dimensional solitons in nonlinear lattices. "Optics letters", Març 2009, vol. 34, núm. 6, p. 770-772.