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

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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.

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Funding

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.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    V. S. Gerdjikov & A. A. Stefanov

  2. National Engineering Physics Institute “MEPhI”, Moscow, Russia

    V. S. Gerdjikov

  3. Faculty of Physics, Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    D. M. Mladenov

  4. Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    A. A. Stefanov

  5. Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    S. K. Varbev

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  1. V. S. Gerdjikov
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Correspondence to V. S. Gerdjikov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 237-260 https://doi.org/10.4213/tmf10049.

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Gerdjikov, V.S., Mladenov, D.M., Stefanov, A.A. et al. The \(\text{m}\)KdV-type equations related to \(A_5^{(1)}\) and \(A_5^{(2)}\) Kac–Moody algebras. Theor Math Phys 207, 604–625 (2021). https://doi.org/10.1134/S0040577921050068

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