In this paper, the Riemann–Hilbert problem of the Sasa–Satsuma higher-order nonlinear Schrödinger equation is investigated, from which spectral and soliton structures are discussed in detail. In addition, an algebra technique is developed to illustrate the soliton structures using Mathematica symbolic computations by choosing suitable parameters, including breather-bell soliton, double-hump soliton, and bell-to-breather soliton interactions. The results show that the spectral and soliton structures of the Sasa–Satsuma higher-order nonlinear Schrödinger equation are more complicated than many other nonlinear Schrödinger type equations.

本文研究了Sasa-Satsuma高阶非线性Schrödinger方程的Riemann-Hilbert问题，从中详细讨论了光谱和孤子结构。此外，还开发了一种代数技术，通过选择合适的参数来使用Mathematica符号计算来说明孤子结构，这些参数包括通气铃-铃孤子，双峰孤子和铃-呼吸孤子相互作用。结果表明，Sasa–Satsuma高阶非线性Schrödinger方程的光谱和孤子结构比许多其他非线性Schrödinger型方程更复杂。