Geodesic
The~$\text{m}$KdV-type equations related to $A_5^{(1)}$ and $A_5^{(2)}$ Kac--Moody algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 237-260

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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. 
@article{TMF_2021_207_2_a5,
     author = {V. S. Gerdjikov and D. M. Mladenov and A. A. Stefanov and S. K. Varbev},
     title = {The~$\text{m}${KdV-type} equations related to $A_5^{(1)}$ and $A_5^{(2)}$ {Kac--Moody} algebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {237--260},
     publisher = {mathdoc},
     volume = {207},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a5/}
}
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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. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 237-260. http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a5/