Lattice solitons supported by competing cubic-quintic nonlinearity

We study various families of lattice solitons supported by competing cubic-quintic nonlinearity, in the framework of NLSE with periodic potential. For the first time to our knowledge, we found 'multi-stable' states in the semi-infinite gap. Linear stability analysis and numerical simulation show that some lattice solitons in the semi-infinite gap are stable, while some are unstable, but they do not radiate. Lattice solitons in higher gaps are unstable except for those single-humped solitons (even symmetry) and two-humped solitons (odd symmetry) with their eigenvalue close to the left band of the gap they reside in.