The mumford dynamical system and the Gelfand--Dikii recursion
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 17-26
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In his paper “The Mumford dynamical system and hyperelliptic Kleinian
functions”
[Funkts. Anal. Prilozhen. 57 (4), 27–45 (2023)]
Victor Buchstaber developed the differential-algebraic theory of
the Mumford dynamical system.
The key object of this theory is the $(P,Q)$-recursion introduced in his paper.
In the present paper, we further develop the theory of the $(P,Q)$-recursion and describe
its connections to the Korteweg–de Vries hierarchy, the
Lenard operator, and the Gelfand–Dikii recursion.
Keywords:
Korteweg–de Vries (KdV) equation, parametric KdV hierarchy, Gelfand–Dikii hierarchy, Lenard operator,
polynomial dynamical systems, polynomial integrals, differential polynomials.
@article{FAA_2023_57_4_a1,
author = {P. G. Baron},
title = {The mumford dynamical system and the {Gelfand--Dikii} recursion},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {17--26},
publisher = {mathdoc},
volume = {57},
number = {4},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a1/}
}
P. G. Baron. The mumford dynamical system and the Gelfand--Dikii recursion. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 17-26. http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a1/