This article is cited in 3 papers

On modified $B$KP systems and generalizations

Zheng Wang^a, Chuanzhong Li<sup>ab

a</sup> School of Mathematics and Statistics, Ningbo University, Ningbo, Zhejiang, China
^b College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, China

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.

Keywords: modified $B$KP hierarchy, Hirota bilinear identity, Fay identity, additional symmetries, multicomponent modified $B$KP hierarchy, noncommutative modified $B$KP hierarchy.

MSC: 37K05, 37K10, 35Q53

Received: 24.03.2021
Revised: 26.04.2021

DOI: 10.4213/tmf10099

 English version: Theoretical and Mathematical Physics, 2021, 209:3, 1693–1716

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