Optical dark solitons in purely cubic-quintic nonlinear lattices

In this work, we establish the existence of different dark soliton families in the nonlinear Schrödinger equation with purely cubic-quintic nonlinear lattices, including individual dark solitons and soliton clusters with varying numbers of valleys. We explore two types of cubic-quintic lattices, the competing lattices (with the nonlinear terms of opposite signs) and the defocusing lattices (with the nonlinear terms of the same signs). The spacing between the valleys of dark soliton clusters is chosen as an integer multiple of the lattice's period. We find that the stability domains of dark solitons in the defocusing lattices are larger than those in the competing lattices. The stability domains of dark soliton families are obtained by linear stability analysis and confirmed by direct numerical simulations. Both stable and unstable propagations of such families are displayed, highlighting the distinct dynamics introduced by these nonlinear interactions and their impact on the formation and stability of dark solitons.