Abstract
This is a short review of the Kadomtsev–Petviashvili hierarchies of types \(\mathrm{B}\) and \(\mathrm{C}\). The main objects are the \(L\) operator, the wave operator, the auxiliary linear problems for the wave function, the bilinear identity for the wave function, and the tau function. All of them are discussed in the paper. Connections with the usual (type-\(\mathrm{A}\)) Kadomtsev–Petviashvili hierarchy are clarified. Examples of soliton solutions and the dispersionless limit of the hierarchies are also considered.
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Acknowledgments
The author thanks V. Akhmedova, I. Krichever, S. Natanzon, and D. Rudneva for discussions.
Funding
This work was supported by the Russian Science Foundation under grant No. 19-11-00275.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 208, pp. 15-38 https://doi.org/10.4213/tmf10072.
Dedicated to the memory of S. M. Natanzon
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Zabrodin, A.V. Kadomtsev–Petviashvili hierarchies of types B and C. Theor Math Phys 208, 865–885 (2021). https://doi.org/10.1134/S0040577921070023
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DOI: https://doi.org/10.1134/S0040577921070023