One-dimensional dark solitons in lattices with higher-order nonlinearities

The existence of dark solitons in the discrete nonlinear Schrödinger equation with third- and fifth-order nonlinearities is investigated. Effects of discreteness for the homogeneous case are analyzed. Exact analytical solutions are found for wide static dark solitons in the presence of impurities. The bound soliton-defect formations can have a single minimum for attractive impurities or two minima for repulsive impurities. In contrast to the standard cubic nonlinear case, where the positions of the minima do not depend on the nonlinearity, now they are strongly influenced by the quintic nonlinearity. The model plays an important role in numerous physical systems with complicated nonlinear interactions