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arXiv · 2311.07341

A KP-mKP Hierarchy via Operators with Two Derivations

Lumin Geng·Jianxun Hu·Chao-Zhong Wu
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Abstract

By using pseudo-differential operators containing two derivations, we extend the Kadomtsev-Petviashvili (KP) hierarchy to a certain KP-mKP hierarchy. For the KP-mKP hierarchy, we obtain its B\"{a}cklund transformations, bilinear equations of Baker-Akhiezer functions and Hirota equations of tau functions. Moreover, we show that this hierarchy is equivalent to a subhierarchy of the dispersive Whitham hierarchy associated to the Riemann sphere with its infinity point and one movable point marked.

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Lumin Geng, Jianxun Hu, Chao-Zhong Wu. 2023-11-13. A KP-mKP Hierarchy via Operators with Two Derivations. https://arxiv.org/abs/2311.07341

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