Nonlinear tunneling of optical similaritons in a tapered graded-index nonlinear waveguide

We consider the nonlinear Schrödinger equation with variable coefficient which describes the beam propagation in an inhomogeneous tapered graded-index nonlinear waveguide. We have obtained exact bright and dark similariton solutions by using similarity transformation and Darboux technique. As an application, we discuss the nonlinear tunneling of optical similaritons for two cases: (i) tunneling with constant background and (ii) tunneling with exponential background. Additionally, we have investigated the case of cascade compression of the pulse. We expect that the results obtained find promising applications in nonlinear optical devices based on optical similaritons.