论文标题
与冈本多项式层次结构相关的流氓波模式
Rogue wave patterns associated with Okamoto polynomial hierarchies
论文作者
论文摘要
我们表明，在可集成的系统中存在新型流氓波模式，这些流氓模式由冈本多项式层次结构的根结构描述。当Rogue Wave解决方案的$τ$函数是三个索引跳跃的Schur多项式的决定因素时，这些流氓模式就会产生。我们在Manakov系统和三波共振的相互作用系统中演示了这些新的流氓模式。对于每个系统，我们通过冈本多项式层次结构在大型内部参数下得出其流氓模式的渐近预测。与先前报道的与Yablonskii-Vorob'ev层次结构相关的流氓模式不同，当前的流氓模式中的一个新功能是，从冈本层次结构多项式的根结构到Rogue模式的形状到Rogue模式的形状仅是线性的，但成为领先顺序，但成为领先顺序。结果，除非基础自由参数非常大，否则当前的流氓模式通常会从冈本根结构中变形，有时会出现很大变形。我们对流氓模式的分析预测与真实的解决方案进行了比较，即使流氓模式从冈本根结构强烈变形时，也可以观察到出色的一致性。
We show that new types of rogue wave patterns exist in integrable systems, and these rogue patterns are described by root structures of Okamoto polynomial hierarchies. These rogue patterns arise when the $τ$ functions of rogue wave solutions are determinants of Schur polynomials with index jumps of three, and an internal free parameter in these rogue waves gets large. We demonstrate these new rogue patterns in the Manakov system and the three-wave resonant interaction system. For each system, we derive asymptotic predictions of its rogue patterns under a large internal parameter through Okamoto polynomial hierarchies. Unlike the previously reported rogue patterns associated with the Yablonskii-Vorob'ev hierarchy, a new feature in the present rogue patterns is that, the mapping from the root structure of Okamoto-hierarchy polynomials to the shape of the rogue pattern is linear only to the leading order, but becomes nonlinear to the next order. As a consequence, the current rogue patterns are often deformed, sometimes strongly deformed, from Okamoto root structures, unless the underlying free parameter is very large. Our analytical predictions of rogue patterns are compared to true solutions, and excellent agreement is observed, even when rogue patterns are strongly deformed from Okamoto root structures.
