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arXiv · 2603.25352

From pencils of Novikov algebras of St\"ackel type to soliton hierarchies

Maciej Błaszak·Krzysztof Marciniak·Błażej M. Szablikowski
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Abstract

In this article we construct evolutionary soliton hierarchies from pencils of Novikov algebras of St\"ackel type. We start by defining a special class of associative Novikov algebras, which we call Novikov algebras of St\"ackel type, as they are associated with classical St\"ackel metrics in Vi\`ete coordinates. We obtain sufficient conditions for pencils of these algebras so that the corresponding Dubrovin-Novikov Hamiltonian operators can be centrally extended, producing sets of pairwise compatible Poisson operators. These operators lead to coupled Korteweg-de~Vries (cKdV) and coupled Harry Dym (cHD) hierarchies, as well as to a triangular cKdV hierarchy and a triangular cHD hierarchy.

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Maciej Błaszak, Krzysztof Marciniak, Błażej M. Szablikowski. 2026-03-26. From pencils of Novikov algebras of St\"ackel type to soliton hierarchies. https://arxiv.org/abs/2603.25352

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