In this paper, we mainly analyze the long-time asymptotics of high-order soliton for the Hirota equation. Two different Riemann–Hilbert representations of Darboux matrices with high-order soliton are given to establish the relationships between inverse scattering method and Darboux transformation. The asymptotic analysis with single spectral parameter is derived through the formulas of determinant directly. Furthermore, the long-time asymptotics with $k$ spectral parameters is given by combining the iterated Darboux matrices and the result of high-order soliton with single spectral parameter, which discloses the structure of high-order soliton clearly and is possible to be utilized in the optic experiments.

本文主要分析Hirota方程高阶孤子的长时间渐近性。给出了具有高阶孤子的 Darboux 矩阵的两种不同的 Riemann-Hilbert 表示，以建立逆散射方法和 Darboux 变换之间的关系。单谱参数渐近分析直接通过行列式公式推导出来。此外，长期渐近线与$克$ 光谱参数是通过迭代达布矩阵和高阶孤子与单个光谱参数的结果相结合给出的，它清楚地揭示了高阶孤子的结构，可以用于光学实验。