A new two-component Sasa–Satsuma equation associated with a \(4\times 4\) matrix spectral problem is proposed by resorting to the zero-curvature equation. Riemann–Hilbert problems are formulated on the basis of spectral analysis of the \(4\times 4\) matrix Lax pair for the two-component Sasa–Satsuma equation, from which zero structures of the Riemann–Hilbert problems are investigated. As applications, N-soliton formulas of the two-component Sasa–Satsuma equation are obtained by solving a particular Riemann–Hilbert problem corresponding to the reflectionless case. Further, the obtained N-soliton formulas are expressed by the ratios of determinants, which are more compact and convenient for symbolic computations. Moreover, the interaction dynamics of the multi-soliton solutions are analyzed and graphically illustrated.

借助于零曲率方程，提出了一个新的与（4 × 4）矩阵光谱问题相关的两成分Sasa-Satsuma方程。黎曼–希尔伯特问题是在对两成分Sasa–Satsuma方程的\（4 × 4 \）矩阵Lax对进行频谱分析的基础上制定的，从中研究了黎曼–希尔伯特问题的零结构。作为应用，通过求解与无反射情况相对应的特定Riemann-Hilbert问题，获得了两组分Sasa-Satsuma方程的N-孤子公式。此外，获得的N孤子公式由行列式的比率表示，行列式更紧凑，更便于符号计算。此外，对多孤子解决方案的相互作用动力学进行了分析和图解说明。