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TMF, 2021 Volume 207, Number 2, Pages 237–260 (Mi tmf10049)

This article is cited 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

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.

Received: 28.12.2020
Revised: 28.12.2020

DOI: 10.4213/tmf10049


 English version:
Theoretical and Mathematical Physics, 2021, 207:2, 604–625

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© Steklov Math. Inst. of RAS, 2024