Exact Solutions and Dynamical Behaviors of the Raman Soliton Model with Anti-Cubic Nonlinearity

This work investigates the exact solutions of the Raman soliton model with anti-cubic nonlinear in optical metamaterials. By travelling wave transformation, the model is transformed into a singular planar dynamical system with three singular straight lines. Using the bifurcation theory 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 "caught in one dragnet".