Dark soliton in the exponentially decaying optical lattice with spatially inhomogeneous Gaussian nonlinearities

In this paper, we numerically study the (1+1)-dimensional inhomogeneous nonlinear Schrödinger (NLS) equation, which describes the propagation of light in the optical lattice with spatially inhomogeneous nonlinearities. The results reveal that in the exponentially decaying optical lattice, the dark soliton induced by spatially inhomogeneous Gaussian nonlinearity could exist. The stability of the dark soliton is also presented under the influence of different inhomogeneous nonlinearities.