In this paper, we study the N-soliton solutions for the Hirota and Maxwell–Bloch equation with physical meaning. From the Lax pair and Volterra integral equations, the Riemann–Hilbert problem of this integrable equation is constructed. By solving the matrix Riemann–Hilbert problem with the condition of no reflecting, the N-soliton solutions for the Hirota and Maxwell–Bloch equation are obtained explicitly. Finally, we simulate the three-dimensional diagram of |E| with 2-soliton solutions and the motion trajectory of t-axis in the case of different z.

中文翻译：

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通过 Riemann-Hilbert 方法对 Hirota 和 Maxwell-Bloch 方程的 N 孤子解

在本文中，我们研究了ñ具有物理意义的 Hirota 和 Maxwell-Bloch 方程的孤子解。从 Lax 对和 Volterra 积分方程，构造了这个可积方程的 Riemann-Hilbert 问题。通过求解无反射条件下的矩阵 Riemann-Hilbert 问题，ñHirota 和 Maxwell-Bloch 方程的 -孤子解是明确获得的。最后，我们模拟了三维图|乙|2孤子解和运动轨迹吨-轴在不同的情况下z.