Generation and controlling of ultrashort self-similar solitons and rogue waves in inhomogeneous optical waveguide

Abstract We present exact bright, dark and rogue soliton solutions of generalized higher-order nonlinear Schrodinger equation, describing the ultrashort beam propagation in tapered waveguide amplifier, via a similarity transformation connected with the constant-coefficient Sasa-Satsuma and Hirota equations. Our exact analysis takes recourse to identify the allowed tapering profile in conjunction with appropriate gain function which corresponds to PT -symmetric waveguide. We extend our analysis to study the effect of tapering profiles and higher-order terms on the evolution of self-similar waves and thus enabling one to control the self-similar wave structure and dynamical behavior.