Dark-gap solitons with mixed nonlinear and linear lattices

We study the existence and stability of dark-gap solitons in linear lattice and nonlinear lattices. The results indicate that the combination of linear and nonlinear lattices gives dark-gap solitons unique properties. The linear lattice can stabilize dark-gap solitons, while the nonlinear lattice reduces the stability of dark-gap solitons. On the basis of numerical analysis, we investigate the effects of lattice depth, chemical potential, nonlinear lattice amplitude, and nonlinear lattice period on the soliton in mixed lattices with the same and different periods. The stability of dark-gap soliton is studied carefully by means of real-time evolution and linear stability analysis. Dark-gap solitons can exist stably in the band gap, but the solitons formed by the mixed lattices are slightly different when the period is the same or different.