The multi-soliton solutions and breathers to the coupled higher-order nonlinear Schrödinger (CH-NLS) equation are derived in this work via the Riemann–Hilbert approach. Firstly, the spectral structure of the CH-NLS equation is investigated and then a matrix Riemann–Hilbert problem on the real axis is strictly formulated. Secondly, by solving the special Riemann–Hilbert problem with no reflection where a jump matrix is taken to be the identity matrix, the formula of N-soliton solutions can be computed. Thirdly, we prove that the higher-order linear and nonlinear term r has important impact on the velocity, phase, period and wavewidth of wave dynamics. Besides, the localized waves characteristics together with collision dynamic behaviors of these explicit soliton solutions and breathers are shown graphically and discussed in detail. Interestingly, three solitons display different dynamics which demonstrate amplitudes of the right-direction waves gradually become larger during the propagation process.

在这项工作中，通过Riemann-Hilbert方法导出了耦合的高阶非线性Schrödinger（CH-NLS）方程的多孤子解和呼吸。首先，研究了CH-NLS方程的光谱结构，然后严格公式化了实轴上的矩阵Riemann-Hilbert问题。其次，通过求解一个无反射的特殊Riemann-Hilbert问题，其中将跳跃矩阵作为恒等矩阵，可以计算N孤立子解的公式。第三，我们证明了高阶线性和非线性项r对波动力学的速度，相位，周期和波长具有重要影响。此外，图形化地显示并详细讨论了这些显式孤子解和呼吸器的局域波特征以及碰撞动力学行为。有趣的是，三个孤子显示出不同的动力学，这些动力学表明右向波的振幅在传播过程中逐渐变大。