Controlling Optical Similaritons in GRIN Waveguide Under the Action of Cubic–Quintic Nonlinear Media

In this chapter, we obtain a family of bright and dark similaritons for the variable coefficient cubic–quintic nonlinear Schrödinger equation, by employing the similarity reductions in two steps. Further, the existence of kink and double-kink similaritons in various parameter domains are delineated. We will be able to tune the amplitude and the propagation distance of similaritons in a tapered graded-index waveguide, by using the cubic nonlinearity coefficient. Additionally, we explicate the mechanism to obtain compressed waves for varying detuning parameters and the coefficient of cubic nonlinearity.