Abstract
We present several kinds of optical solitary wave solutions for the fourth-order dispersive cubic-quintic nonlinear Schrödinger equation describing the propagation of optical pulses in a medium that exhibits a parabolic nonlinearity law. Among them, apart from some regular fundamental bright solitary wave solutions and dark solitary wave solutions given, there are also two kinds of combined solitary wave solutions, i.e., bright and dark solitary wave and W-shaped solitary wave solutions which describe bright and dark solitary wave properties. It is found that their amplitude may approach nonzero when the time variable approaches infinity. Moreover, when the parameters of the bright and dark solitary wave are selected appropriately, the kink and anti-kink solitary wave solutions, which are first reported in the fourth-order dispersive cubic-quintic nonlinear Schrödinger equation, are discovered.
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