Riemann–Hilbert approach and nonlinear dynamics of the coupled higher-order nonlinear Schrödinger equation in the birefringent or two-mode fiber
Riemann–Hilbert approach and nonlinear dynamics of the coupled higher-order nonlinear Schrödinger equation in the birefringent or two-mode fiber
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DOI：
10.1007/s11071-021-06286-6
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发表时间：
2021-02
影响因子：
5.6
通讯作者：
Han-yu Wei;E. Fan;Han-Dong Guo
中科院分区：
文献类型：
--
作者：
Han-yu Wei;E. Fan;Han-Dong Guo
利用Riemann-Hilbert方法导出了耦合高阶非线性薛定谔方程的多孤子解和呼吸子。首先研究了CH-NLS方程的谱结构，然后严格地构造了真实的轴上的矩阵Riemann-Hilbert问题。其次，通过求解特殊的无反射Riemann-Hilbert问题，其中跳跃矩阵是单位矩阵，可以计算出N-孤子解的公式。第三，证明了高阶线性项和非线性项对波动力学的速度、相位、周期和波宽有重要影响。此外，还用图形的方法给出了这些孤立子解和呼吸子的局域波特征和碰撞动力学行为，并进行了详细的讨论。有趣的是，三个孤子表现出不同的动力学，这表明在传播过程中的右向波的振幅逐渐变大。
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 ofN-soliton solutions can be computed. Thirdly, we prove that the higher-order linear and nonlinear termrhas 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.