Symmetric and antisymmetric solitons in finite lattices

We propose a simple model for the realization of symmetrically and antisymmetrically shape-preserving nonlinear waves with nonvanishing intensities at infinity. A finite lattice embedded into a defocusing saturable medium can support various families of novel solitons, including out-of-phase and in-phase solitons with symmetric and antisymmetric profiles. Although the lattice is finite, the existence and stability of solitons depend strongly on the band-gap structure of the corresponding infinite lattice. Saturable nonlinearity enhances the pedestal height and renormalized energy flow of solitons evidently. In particular, increasing the lattice site number or saturation degree of nonlinearity can considerably suppresses the instability of solitons. In addition, we find two branches of in-phase solitons in finite lattices and one branch of them can be dynamically stable. Our findings may provide a helpful hint for linking the solitons supported by infinite and finite lattices.