Riccati parameterized self-similar waves in two-dimensional graded-index waveguide

An analytical method based on gauge-similarity transformation technique has been employed for mapping a (2+1)- dimensional variable coefficient coupled nonlinear Schrödinger equations (vc-CNLSE) with dispersion, nonlinearity and gain to standard NLSE. Under certain functional relations we construct a large family of self-similar waves in the form of bright similaritons, Akhmediev breathers and rogue waves. We report the effect of dispersion on the intensity of the solitary waves. Further, we illustrate the procedure to amplify the intensity of self-similar waves using isospectral Hamiltonian approach. This approach provides an efficient mechanism to generate analytically a wide class of tapering profiles and widths by exploiting the Riccati parameter. Equivalently, it enables one to control efficiently the self-similar wave structures and hence their evolution.