一、引言 光纤中的孤立波概念最先是由光纤通讯的发展而引进的。由于光信号在光纤传输中发生展宽、畸变,光信号传输速率受到限制。在1973年,Hasegawa和Tappert提出用介质的非线性效应补偿它的色散,二者达到平衡后,便形成稳定非线性波,此即孤立波。稍后,便得到了描述孤立波在理想单模光纤中传播的非线性薛定谔方程。利用逆散射方法可以求解。据现有的文献,已给出N=1、2孤立波的解析表达式,给出了N=1、2、3的孤立波波形图。本文通过求解秩很高的逆散射函数方程 I. INTRODUCTION The concept of solitary wave in optical fiber was first introduced by the development of optical fiber communication. As the optical signal in the optical fiber transmission occurs in the broadening, distortion, optical signal transmission rate is limited. In 1973, Hasegawa and Tappert proposed compensating for their dispersion with the nonlinear effect of the medium, and when they reached equilibrium, they formed a stable nonlinear wave, that is, a solitary wave. Later, a nonlinear Schrödinger equation describing the propagation of solitary waves in a perfect single-mode fiber was obtained. Using the inverse scattering method can be solved. According to the existing literature, the analytical expressions of N = 1, 2 solitary waves are given, and the solitary waveforms of N = 1,2,3 are given. In this paper, we solve the high order inverse scattering function equation