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Bilinear Equation and Additional Symmetries for an Extension of the Kadomtsev–Petviashvili Hierarchy

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Abstract

An extension of the Kadomtsev–Petviashvili (KP) hierarchy defined via scalar pseudo-differential operators was studied in Szablikowski and Blaszak (J. Math. Phys. 49(8), 082701, 20, 2008) and Wu and Zhou (J. Geom. Phys. 106, 327–341, 2016). In this paper, we represent the extended KP hierarchy into the form of bilinear equation of (adjoint) Baker–Akhiezer functions, and construct its additional symmetries. As a byproduct, we derive the Virasoro symmetries for the constrained KP hierarchies.

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Acknowledgements

The authors thank Professor Baofeng Feng for helpful discussions. This work is partially supported by the National Natural Science Foundation of China Nos. 12022119, 11771461, 11831017 and 11521101.

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Correspondence to Chao-Zhong Wu.

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Communicated by: Youjin Zhang

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Lu, J., Wu, CZ. Bilinear Equation and Additional Symmetries for an Extension of the Kadomtsev–Petviashvili Hierarchy. Math Phys Anal Geom 24, 27 (2021). https://doi.org/10.1007/s11040-021-09401-6

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  • DOI: https://doi.org/10.1007/s11040-021-09401-6

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