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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 2, Pages 237–260
DOI: https://doi.org/10.4213/tmf10049 (Mi tmf10049) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The $\text{m}$KdV-type equations related to $A_5^{(1)}$ and $A_5^{(2)}$ Kac–Moody algebras

V. S. Gerdjikovab, D. M. Mladenovc, A. A. Stefanovad, S. K. Varbeve

a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
b National Engineering Physics Institute "MEPhI", Moscow, Russia
c Faculty of Physics, Sofia University ``St. Kliment Ohridski'', Sofia, Bulgaria
d Faculty of Mathematics and Informatics, Sofia University "St. Kliment Ohridski", Sofia, Bulgaria
e Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria
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DOI: https://doi.org/10.4213/tmf10049
Abstract: We explain the details of the algebraic constructions on nontrivial examples of the mKdV equations related to the $A_5^{(1)}$ and $A_5^{(2)}$ Kac–Moody algebras. Several types of recursion operators appear naturally in formulating the equations and their Hamiltonian structures. We next introduce the resolvent of the Lax operator and demonstrate that it generates the hierarchy of the Lax representations and also the hierarchy of conservation laws of these equations.
Keywords: mKdV equation, recursion operator, Kac–Moody algebra, hierarchy of integrable equations.
Funding agency Grant number
Bulgarian National Science Fund DN 18/3
KP-06N42-2
Ministry of Education and Science of Bulgaria 577/17.08.2018
The research of V. S. Gerdjikov is supported by the Bulgarian National Science Foundation (Contract No. KP-06N42-2). The research of D. M. Mladenov was supported in part by the Bulgarian National Science Fund (Research Grant No. DN 18/3). The research of A. A. Stefanov was supported in part by the Bulgarian National Science Fund (Research Grant No. DN 18/3) and the Bulgarian National Science Foundation (Contract No. KP-06N42-2). The research of S. K. Varbev is supported by the Bulgarian Ministry of Education and Science under the National Research Programme “Young scientists and postdoctoral researchers” approved by DCM No. 577/17.08.2018.
Received: 28.12.2020
Revised: 28.12.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 2, Pages 604–625
DOI: https://doi.org/10.1134/S0040577921050068
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. S. Gerdjikov, D. M. Mladenov, A. A. Stefanov, S. K. Varbev, “The $\text{m}$KdV-type equations related to $A_5^{(1)}$ and $A_5^{(2)}$ Kac–Moody algebras”, TMF, 207:2 (2021), 237–260; Theoret. and Math. Phys., 207:2 (2021), 604–625
Citation in format AMSBIB
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\paper The~$\text{m}$KdV-type equations related to $A_5^{(1)}$ and $A_5^{(2)}$ Kac--Moody algebras
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\pages 237--260
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\jour Theoret. and Math. Phys.
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\pages 604--625
\crossref{https://doi.org/10.1134/S0040577921050068}
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    • This publication is cited in the following 3 articles:
    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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