Zhang Guoqiang, Yan Zhenya, Wang Li
Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China.
Proc Math Phys Eng Sci. 2019 Feb;475(2222):20180625. doi: 10.1098/rspa.2018.0625. Epub 2019 Feb 6.
The general coupled Hirota equations are investigated, which describe the wave propagations of two ultrashort optical fields in a fibre. Firstly, we study the modulational instability for the focusing, defocusing and mixed cases. Secondly, we present a unified formula of high-order rational rogue waves (RWs) for the focusing, defocusing and mixed cases, and find that the distribution patterns for novel vector rational RWs of focusing case are more abundant than ones in the scalar model. Thirdly, the th-order vector semirational RWs can demonstrate the coexistence of th-order vector rational RWs and breathers. Fourthly, we derive the multi-dark-dark solitons for the defocsuing and mixed cases. Finally, we derive a formula for the coexistence of dark solitons and RWs. These results further enrich and deepen the understanding of localized wave excitations and applications in vector nonlinear wave systems.
研究了一般耦合的广田方程，该方程描述了光纤中两个超短光场的波传播。首先，我们研究了聚焦、散焦和混合情况下的调制不稳定性。其次，我们给出了聚焦、散焦和混合情况下高阶有理 rogue 波（RWs）的统一公式，并发现聚焦情况下新型矢量有理 RW 的分布模式比标量模型中的更为丰富。第三，第(n)阶矢量半有理 RW 可以展示第(n)阶矢量有理 RW 和呼吸子的共存。第四，我们推导了散焦和混合情况下的多暗-暗孤子。最后，我们推导了暗孤子和 RW 共存的公式。这些结果进一步丰富和深化了对矢量非线性波系统中局域波激发及其应用的理解。
