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- W4308829830 abstract "In this paper, we study the general rogue wave solutions and their patterns in the vector (or $M$-component) nonlinear Schr{o}dinger (NLS) equation. By applying the Kadomtsev-Petviashvili hierarchy reduction method, we derived an explicit solution for the rogue wave expressed by $tau$ functions that are determinants of $Ktimes K$ 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." @default.
- W4308829830 created "2022-11-16" @default.
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- W4308829830 date "2022-11-10" @default.
- W4308829830 modified "2023-10-06" @default.
- W4308829830 title "Rogue waves and their patterns in the vector nonlinear Schr{o}dinger equation" @default.
- W4308829830 doi "https://doi.org/10.48550/arxiv.2211.05603" @default.
- W4308829830 hasPublicationYear "2022" @default.
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