Abstract
We present exact bright, dark and rogue soliton solutions of generalized higher-order nonlinear Schrödinger 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.
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