This paper investigates Raman soliton model in optical metamaterials, having anti-cubic nonlinearity. By travelling wave transformation, the model is transformed into a singular planar dynamical system having three singular straight lines. Using the bifurcation theory method of dynamical systems, under different parameter conditions, bifurcations of phase portraits are studied. More than 30 exact explicit solutions of planar dynamical system are derived, such as exact periodic wave solutions, solitary wave solutions, kink and anti-kink wave solutions, periodic peakons and peakons as well as compacton solutions. In more general parametric conditions, all possible solutions are found.