Controlling Similaritons in Two-Dimensional GRIN Waveguide Through Riccati Parameter

In this chapter, we employ an analytical method based on the gauge-similarity transformation technique for mapping a (2+1)-dimensional variable coefficient coupled nonlinear Schrödinger equations (vc-CNLSE) with dispersion, nonlinearity, and gain to canonical NLSE. We have constructed different varieties of self-similar waves in the form of bright similaritons, Akhmediev breathers, and rogue waves, subjected to certain restrictive functional relations. We report the effect of dispersion on the intensity of the solitary waves. By using the isospectral Hamiltonian approach, we illustrate the amplification of the intensity of self-similar waves. This approach results in generating analytically a wide class of tapering profiles and widths by exploiting the Riccati parameter. Thereby, this mechanism helps in controlling efficiently the self-similar wave structures and hence their evolution.