Controllable nonautonomous waves in tapered graded-index waveguides -- Controllable optical similaritons in GRIN by tailoring of tapered profile -- Butterfly-shaped and dromion-like waves in GRIN waveguid -- Controlling optical similaritons in GRIN waveguide under the action of cubic-quintic nonlinear media -- Dynamics of optical rogue waves in a GRIN waveguide with different background beams -- Controlling similaritons in two-dimensional GRIN waveguide through Riccati parameter -- Symbiotic rogons in (2+1)-dimensional GRIN waveguide -- Conclusions and future perspectives.

This book highlights the dynamical behavior of self-similar waves in graded-index waveguides in (1+1)-dimensions and (2+1)-dimensions. The mechanism to control these optical similaritons by tailoring the tapering profile is presented. Various nonlinear waves like rogons, butterfly-shaped, and dromion-like waves and their controllable behavior are discussed in detail. The phenomenon of unbreakable Parity-Time symmetry of some of these waves has been delineated for different variety of solvable potentials. Compression of these exotic waves has been demonstrated for dispersion decreasing fiber and periodic management of dispersion and nonlinearity parameters. Competing cubic-quintic nonlinearity scenario and its potential implication on the dynamics of these similaritons has been described in detail. Symbiotic self-similar rogue waves have been discussed in (2+1)-dimensional garded-index waveguide. The book also includes numerical simulations that complement these analytical insights.