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- W4324358765 abstract "Abstract 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." @default.
- W4324358765 created "2023-03-16" @default.
- W4324358765 creator A5050415148 @default.
- W4324358765 creator A5054430698 @default.
- W4324358765 date "2023-03-15" @default.
- W4324358765 modified "2023-10-13" @default.
- W4324358765 title "Rogue wave patterns associated with Okamoto polynomial hierarchies" @default.
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- W4324358765 doi "https://doi.org/10.1111/sapm.12573" @default.
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