Rogue wave patterns associated with Okamoto polynomial hierarchies
Rogue wave patterns associated with Okamoto polynomial hierarchies
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DOI：
10.1111/sapm.12573
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发表时间：
2022-08
影响因子：
2.7
通讯作者：
Bo Yang;Jianke Yang
中科院分区：
文献类型：
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作者：
Bo Yang;Jianke Yang
我们发现，新类型的流氓波图案存在于可积系统中，这些流氓图案的冈本多项式族的根结构描述。当流氓波解的τ函数是指数跳为3的Schur多项式的行列式时，并且这些流氓波中的内部自由参数变大时，就会出现这些流氓图案。我们在马纳科夫系统和三波共振相互作用系统中展示了这些新的流氓模式。对于每一个系统，我们推导出一个大的内部参数下，通过冈本多项式层次的流氓模式的渐近预测。与先前报道的与Yablonskiii-Vorob 'ev层级相关联的流氓模式不同，本流氓模式中的新特征是从Okamoto层级多项式的根结构到流氓模式的形状的映射仅对首阶是线性的，但对下一阶变得非线性。因此，当前的流氓模式通常是变形的，有时强烈变形，从冈本层次根结构，除非潜在的内部参数非常大。我们的流氓模式的分析预测进行比较，真正的解决方案，并观察到良好的协议，即使流氓模式强烈变形从冈本层次根结构。
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‐hierarchy root structures, unless the underlying internal 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‐hierarchy root structures.