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On modified \(B\)KP systems and generalizations

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Abstract

We find the form of the Orlov–Schulman operator of the modified \(B\)KP hierarchy, which played a pivotal role in the construction of additional symmetries for the modified \(B\)KP hierarchy. We investigate the tau functions of the modified \(B\)KP hierarchy and give many interesting properties, including Hirota bilinear identities and \((\)differential\()\) Fay identities. We also present the multicomponent modified \(B\)KP hierarchy and define a series of additional flows of the multicomponent modified \(B\)KP hierarchy that constitute an \(N\)-fold direct product of the positive half of the quantum torus symmetries. Finally, we introduce the noncommutative modified \(B\)KP hierarchy and derive its symmetries, as we do for the multicomponent modified \(B\)KP hierarchy.

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Funding

Chuanzhong Li is supported by the National Natural Science Foundation of China under Grant no. 12071237 and K. C. Wong Magna Fund in Ningbo University.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, Zhejiang, China

    Zheng Wang & Chuanzhong Li

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, China

    Chuanzhong Li

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  1. Zheng Wang
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  2. Chuanzhong Li
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Correspondence to Chuanzhong Li.

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The authors declare no conflicts of interest.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 209, pp. 438–464 https://doi.org/10.4213/tmf10099.

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Wang, Z., Li, C. On modified \(B\)KP systems and generalizations. Theor Math Phys 209, 1693–1716 (2021). https://doi.org/10.1134/S0040577921120047

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