论文标题
流氓波及其在矢量非线性schrödinger方程中的模式
Rogue waves and their patterns in the vector nonlinear Schrödinger equation
论文作者
论文摘要
在本文中，我们研究了一般的流氓波解决方案及其模式在向量（或$ m $ - 组件）非线性Schrödinger（NLS）方程中。通过应用kadomtsev-petviaShvili层次结构减少方法，我们得出了由$ k \ times k $ block矩阵（$ k = 1,2，\ cdots，m $）的$ k \ times k $ block矩阵（$ k \ times k $ block矩阵的决定因素）的明确解决方案，其索引跳高为$ m+m+m+1 $ $。彻底研究了流氓波的模式，$ m = 3,4 $和$ k = 1 $。我们发现，当特定的内部参数足够大时，波模式与广义的Wronskian-Hermite多项式层次结构相关，与标量NLS方程，Manakov系统等的流氓波模式相反。此外，广义的Wronskian-Hermite多项式层次结构包括Yablonskii-Vorob'EV多项式层次结构和冈本多项式层次结构作为特殊情况，这些情况用于描述标量NLS方程和Manakov系统的流氓波模式。结果，对于标量NLS方程和Manakov系统，我们扩展了Yang {\ it等}的最新结果。注意到，$ m = 3 $的情况显示了与先前结果不同的新功能。将预测的流氓波模式与两种情况的真正解决方案的$ M = 3,4 $进行了比较。达成了一个很好的协议。
In this paper, we study the general rogue wave solutions and their patterns in the vector (or $M$-component) nonlinear Schrödinger (NLS) equation. By applying the Kadomtsev-Petviashvili hierarchy reduction method, we derived an explicit solution for the rogue wave expressed by $τ$ functions that are determinants of $K\times K$ block matrices ($K=1,2,\cdots, M$) with an index jump of $M+1$. Patterns of the rogue waves for $M=3,4$ and $K=1$ are thoroughly investigated. We find that when a specific internal parameter is large enough, the wave patterns are linked to the root structures of generalized Wronskian-Hermite polynomial hierarchy in contrast with rogue wave patterns of the scalar NLS equation, the Manakov system and many others. Moreover, the generalized Wronskian-Hermite polynomial hierarchy includes the Yablonskii-Vorob'ev polynomial hierarchy and Okamoto polynomial hierarchies as special cases, which have been used to describe the rogue wave patterns of the scalar NLS equation and the Manakov system, respectively. As a result, we extend the most recent results by Yang {\it et al.} for the scalar NLS equation and the Manakov system. It is noted that the case $M=3$ displays a new feature different from the previous results. The predicted rogue wave patterns are compared with the ones of the true solutions for both cases of $M=3,4$. An excellent agreement is achieved.
