论文标题
流氓波的普遍模式
Universal patterns of rogue waves
论文作者
论文摘要
分析研究了非线性Schrödinger（NLS）方程和衍生NLS方程的流氓波模式。结果表明，当这些流氓波的分析表达式中的自由参数很大时，这些波将显示出相同的模式，包括基本的流氓波，形成透明的几何结构，例如三角形，五角大楼，七肠和nonagon和nonagon，并具有可能的低阶流氓在其中心。这些流氓模式由Yablonskii-Vorob'EV多项式层次结构的根结构进行分析确定，其方向由大型自由参数的阶段控制。 Rogue波模式与Yablonskii-Vorob'EV多项式层次结构的根系结构的这种联系超出了NLS和衍生NLS方程，并在可集成系统中引起了普遍的流氓波模式。
Rogue wave patterns in the nonlinear Schrödinger (NLS) equation and the derivative NLS equation are analytically studied. It is shown that when the free parameters in the analytical expressions of these rogue waves are large, these waves would exhibit the same patterns, comprising fundamental rogue waves forming clear geometric structures such as triangle, pentagon, heptagon and nonagon, with a possible lower-order rogue wave at its center. These rogue patterns are analytically determined by the root structures of the Yablonskii-Vorob'ev polynomial hierarchy, and their orientations are controlled by the phase of the large free parameter. This connection of rogue wave patterns to the root structures of the Yablonskii-Vorob'ev polynomial hierarchy goes beyond the NLS and derivative NLS equations, and it gives rise to universal rogue wave patterns in integrable systems.
