Conclusions and Future Perspectives

In this book, we have dealt with the study of exact and numerical self-similar waves that propagate through the GRIN waveguide. We have found bright and dark as well as rogue waves and rogle triplets in diverse media such as competing cubic–quintic nonlinearities and their effect on the ensuing waves. The study of the dynamical behavior of similaritons in graded-index waveguide is very interesting. We have studied nonautonomous wave propagation in the graded-index (GRIN) waveguide for different tapering profiles. To fulfill this task, we have used a multi-variate similarity transformation, which maps the inhomogeneous generalized nonlinear Schrödinger equation to the standard nonlinear Schrödinger equation. We have shown here that these different tapering profiles can support both bright and dark similaritons with significantly high intensity. Particularly, we have studied the dynamical behavior of bright and dark similaritons for three different sets of tapering profiles and widths. Interestingly, in the case of periodic width and tapering profile, we have observed that the similariton gets annihilated and regenerated after some time during its evolution, along the length of the waveguide.