Lax formulation of 3--component KP hierarchy by Shiota construction

Tongtong Cui; Jinbiao Wang; Wenqi Cao; Jipeng Cheng

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arXiv · 2407.21334

Lax formulation of 3--component KP hierarchy by Shiota construction

Tongtong Cui·Jinbiao Wang·Wenqi Cao·Jipeng Cheng

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Abstract

It is quite basic in integrable systems to deriving 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 $\Lambda_1$ and $\Lambda_2$, 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.

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BibTeX RIS

Tongtong Cui, Jinbiao Wang, Wenqi Cao, Jipeng Cheng. 2024-07-31. Lax formulation of 3--component KP hierarchy by Shiota construction. https://arxiv.org/abs/2407.21334

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