In this paper, approximate bright-soliton solutions of the higher-order nonlinear Schrdinger equation are constructed by treating the higher-order terms as small perturbations. The first-, second-, and third-order asymptotic solutions are obtained. The errors between the asymptotic solutions and the numerical/analytical solutions are discussed, which gives a high accuracy of the approximate solutions. It is pointed that the asymptotic solutions can be used as the initial value to improve the accuracy of the numerical solutions. This paper may be helpful for undergraduate and graduate students in mathematics and physics to understand the approximate soliton solutions of the higher-order nonlinear Schrdinger equation.

在本文中，通过将高阶项视为小扰动，构造了高阶非线性Schrdinger方程的近似亮孤子解。获得一阶，二阶和三阶渐近解。讨论了渐近解与数值/解析解之间的误差，从而给出了近似解的高精度。指出可以将渐近解用作初始值，以提高数值解的精度。本文对于数学和物理的本科生和研究生来说，有助于理解高阶非线性Schrdinger方程的近似孤子解。