We investigate higher-order nonlinear Schrödinger-Maxwell-Bloch equations using the Riemann-Hilbert method. We perform a spectral analysis of the Lax pair and construct a Riemann-Hilbert problem according to the spectral analysis. As a result, we obtain three types of multisoliton solutions. Based on the analytic solution and with a choice of corresponding parameter values, we obtain solutions of the breather type and a bell-shaped solution and find an interesting phenomenon of the collision of two soliton solutions. We hope that these results can be useful in modeling the wave propagation of a nonlinear optical field in an erbium-doped fiber medium.

中文翻译：

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高阶非线性薛定谔-麦克斯韦-布洛赫方程的逆散射变换和孤子分类

我们使用 Riemann-Hilbert 方法研究高阶非线性 Schrödinger-Maxwell-Bloch 方程。我们对 Lax 对进行谱分析，并根据谱分析构造一个 Riemann-Hilbert 问题。结果，我们获得了三种类型的多孤子解决方案。基于解析解并选择相应的参数值，我们获得了呼吸器类型的解和钟形解，并发现了两个孤子解碰撞的有趣现象。我们希望这些结果可用于模拟掺铒光纤介质中非线性光场的波传播。