  We present exact bright, dark and rogue soliton solutions of generalized
higherorder 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.
