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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 208, Number 1, Pages 15–38
DOI: https://doi.org/10.4213/tmf10072 (Mi tmf10072) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Kadomtsev–Petviashvili hierarchies of types B and C

A. V. Zabrodin

Skolkovo Institute of Science and Technology, Moscow, Russia
Full-text PDF (522 kB) Citations (11)
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DOI: https://doi.org/10.4213/tmf10072
Abstract: This is a short review of the Kadomtsev–Petviashvili hierarchies of types B and 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-A) Kadomtsev–Petviashvili hierarchy are clarified. Examples of soliton solutions and the dispersionless limit of the hierarchies are also considered.
Keywords: Kadomtsev–Petviashvili hierarchies, tau function, soliton solutions.
Funding agency Grant number
Russian Science Foundation 19-11-00275
This work was supported by the Russian Science Foundation under grant No 19-11-00275).
Received: 04.02.2021
Revised: 04.02.2021
English version:
Theoretical and Mathematical Physics, 2021, Volume 208, Issue 1, Pages 865–885
DOI: https://doi.org/10.1134/S0040577921070023
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Zabrodin, “Kadomtsev–Petviashvili hierarchies of types B and C”, TMF, 208:1 (2021), 15–38; Theoret. and Math. Phys., 208:1 (2021), 865–885
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    1. Shen Wang, Wenchuang Guan, Jipeng Cheng, “Tau functions of modified CKP hierarchy”, Journal of Geometry and Physics, 207 (2025), 105367  crossref
    2. Shen Wang, Wenchuang Guan, Jipeng Cheng, “Bosonic construction of CKP tau function”, Nonlinearity, 38:1 (2025), 015009  crossref
    3. Haiyan Kang, Shen Wang, Jipeng Cheng, “BCr: reductions of modified KP hierarchy”, Anal.Math.Phys., 15:3 (2025)  crossref
    4. Yi Yang, Jipeng Cheng, “Bogoyavlensky–modified KdV hierarchy and toroidal Lie algebra sltor2”, Lett Math Phys, 114:2 (2024)  crossref
    5. Yue Liu, Xingjie Yan, Jinbiao Wang, Jipeng Cheng, “Generalized bigraded Toda hierarchy”, Journal of Mathematical Physics, 65:10 (2024)  crossref
    6. Wenchuang Guan, Shen Wang, Wenjuan Rui, Jipeng Cheng, “Lax structure and tau function for large BKP hierarchy”, Lett Math Phys, 115:1 (2024)  crossref
    7. A. V. Zabrodin, V. V. Prokofev, “Tau-function of the B-Toda hierarchy”, Theoret. and Math. Phys., 217:2 (2023), 1673–1688  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    8. A. Zabrodin, “Quasi-periodic solutions to hierarchies of nonlinear integrable equations and bilinear relations”, Journal of Geometry and Physics, 193 (2023), 104990  crossref  mathscinet
    9. T. V. Redkina, A. R. Zakinyan, R. G. Zakinyan, O. B. Surneva, “Hierarchies of the Korteweg–de Vries equation related to complex expansion and perturbation”, Axioms, 12:4 (2023), 371  crossref
    10. I. Krichever, A. Zabrodin, “Toda lattice with constraint of type B”, Physica D: Nonlinear Phenomena, 453 (2023), 133827  crossref
    11. A. V. Zabrodin, T. Takebe, “Dispersionless version of the constrained Toda hierarchy and symmetric radial Löwner equation”, Lett. Math. Phys., 112 (2022), 105–25  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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