论文标题
三级耦合的麦克斯韦方程：流氓波，半流氓波和W形孤子
The three-level coupled Maxwell-Bloch equations: rogue waves, semirational rogue waves and W-shaped solitons
论文作者
论文摘要
在本文中，通过Darboux转换研究了具有相干三级原子的光学介质中两种光脉冲的传播的耦合Maxwell-Bloch方程。一般的n级流氓波解涉及光谱特征方程的多个根和多种基根的两种不同选择和多参数n-ther-sermiratation溶液的选择。提供了从第一到二阶的显式流氓波解决方案和半疗法解决方案。与已知的公共孤子，深色和四元结构相比，提出了一些不寻常的模式，例如三孔，扭曲对，复合四元和复合的深色流氓波。此外，显示了黑亮孤儿与黑暗流氓波之间的相互作用以及呼吸器和黑暗流氓波之间的相互作用。此外，提出了具有三重和四倍的时间空间分布的高阶非线性叠加模式。最后，发现在低扰动频率下调制不稳定性生长速率趋于零，流氓波和W形孤子之间的状态过渡。特别是检查了深色和双峰W形孤子。
In this paper the coupled Maxwell-Bloch equations which describe the propagation of two optical pulses in an optical medium with coherent three-level atoms are studied by Darboux transformation. The general nth-order rogue wave solution involving two different choices of multiple roots for the spectral characteristic equation and the multiparametric nth-order semirational solution are both obtained in terms of Schur polynomials. The explicit rogue wave solutions and semirational solutions from first to second order are provided. In contrast to the known Peregrine soliton, dark and four-petaled structures, some unusual patterns such as triple-hole, twisted-pair, composite four-petaled and composite dark rogue waves are put forward. Moreover, the interaction between dark-bright soliton and dark rogue wave and interaction between breather and dark rogue wave are shown. Further, the higher-order nonlinear superposition modes which feature triple and quadruple temporal-spatial distributions are presented. Finally, the state transition between rogue wave and W-shaped soliton is found where the modulation instability growth rate tends to zero under the low perturbation frequency. Particularly, the dark and double-peak W-shaped solitons are examined.
