Nonlinearly chirped self-similar waves on a cw background in inhomogeneous long optical waveguide

In this paper, we investigate the propagation of short pulses in an inhomogeneous long optical fibre within the framework of a generalized nonlinear Schro dinger equation with an additional distributed nonlinear correction term involving the time derivative of the pulse envelope and linear gain or loss. A class of nonlinear wave solutions is derived for the first time via a transformation connected with the constant-coefficient Chen-Lee-Liu-type nonlinear Schrodinger equation. These structures possess a number of attractive features such as a self-similarity in pulse shape, a nonlinear behaviour in pulse chirp, localization in structure and a non-zero background. We demonstrate that the presence of self-steepening nonlinearity in the inhomogeneous optical material makes self-similar solitons present an extra frequency chirping property that is directly proportional to the intensity of the wave. The conditions on the optical fibre parameters for the existence of these nonlinearly chirped self-similar localized pulses are presented. As a practical example, we investigate their propagation dynamics in a specified soliton control system. The results are useful in the design of transmission lines with spatial parameter variations and give an effective support for the realization of nonlinearly chirped self-similar solitons on a continuous-wave (cw) background in experiment.