Geodesic
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. 
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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/