In this paper, we investigate the propagation of short pulses in an inhomogeneous long optical fibre within the framework of a generalized nonlinear Schrö 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 Schrödinger 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.

在本文中，我们在广义非线性薛定谔方程的框架内研究了短脉冲在非均匀长光纤中的传播，该方程具有额外的分布式非线性校正项，其中涉及脉冲包络的时间导数和线性增益或损耗。通过与常系数陈-李-刘型非线性薛定谔方程相关联的变换，首次推导出一类非线性波解。这些结构具有许多吸引人的特征，例如脉冲形状的自相似性、脉冲啁啾的非线性行为、结构的局部化和非零背景。我们证明了非均匀光学材料中自陡峭非线性的存在使得自相似孤子呈现出与波的强度成正比的额外频率啁啾特性。给出了这些非线性啁啾自相似定域脉冲存在的光纤参数条件。作为一个实际例子，我们研究了它们在指定孤子控制系统中的传播动力学。研究结果可用于空间参数变化的传输线设计，为实验中在连续波（cw）背景下实现非线性啁啾自相似孤子提供有效支持。给出了这些非线性啁啾自相似定域脉冲存在的光纤参数条件。作为一个实际例子，我们研究了它们在指定孤子控制系统中的传播动力学。研究结果可用于空间参数变化的传输线设计，为实验中在连续波（cw）背景下实现非线性啁啾自相似孤子提供有效支持。给出了这些非线性啁啾自相似定域脉冲存在的光纤参数条件。作为一个实际例子，我们研究了它们在指定孤子控制系统中的传播动力学。研究结果可用于空间参数变化的传输线设计，为实验中在连续波（cw）背景下实现非线性啁啾自相似孤子提供有效支持。