Lax Formulation of 3-Component KP Hierarchy by Shiota Construction

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发表日期：

2025年7月17日

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Tongtong Cui,
Jinbiao Wang,
Wenqi Cao,
Jipeng Cheng

摘要

It is quite basic in integrable systems to derive Lax equations from bilinear equations. For multi-component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases. Here we use Shiota method to construct Lax structure of 3-component KP hierarchy and its reduction by introducing two shift operators $\Lambda _1$ $Λ_{1}$ and $\Lambda _2$ $Λ_{2}$ , where relations among different discrete variables can be easily found. We believe the results here are quite typical for general multi-component KP theory, which may be helpful for general cases.