The KdV-type equations related to and Kac–Moody algebras

We explain the details of the algebraic constructions on nontrivial examples of the mKdV equations related to the and 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 op...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2021, Vol.207 (2), p.604-625
Main Authors: Gerdjikov, V. S., Mladenov, D. M., Stefanov, A. A., Varbev, S. K.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Algebra
Applications of Mathematics
Conservation laws
Mathematical analysis
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We explain the details of the algebraic constructions on nontrivial examples of the mKdV equations related to the and 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.
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577921050068