@inproceedings{d7340153626c48159c5a93ee26d0a784,
title = "New Dubrovin-type integrability theory applications of differential rings",
abstract = "We present a new and effective approach to studying differential- algebraic relationships by means of specially constructed finitely-generated in- variant subrings in differential rings. Based on their properties, we reana- lyzed the Dubrovin integrability criterion for the Riemann type differential- functional constraints, perturbed by means of some elements from a suit- ably constructed differential ring. We also studied invariant finitely-generated ideals naturally related with constraints, generated by the corresponding Lie- algebraic endomorphic representations of derivations on differential ideals and which are equivalent to the corresponding differential-functional relationships on a generating function. The work in part generalizes the results devised before for proving integrability of the well known generalized hierarchy of the Riemann.",
keywords = "Differential geometry, covering mappings, differential algebra, differential equations, differential ideals",
author = "Artemovych, {Orest D.} and Blackmore, {Denis L.} and Kycia, {Radosl A.} and Prykarpatski, {Anatolij K.}",
note = "Publisher Copyright: {\textcopyright} 2023 American Mathematical Society.; Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, 2021 ; Conference date: 13-12-2021 Through 17-12-2021",
year = "2023",
doi = "10.1090/conm/789/15838",
language = "English (US)",
isbn = "9781470473556",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "19--39",
editor = "I.S. Krasil{\textquoteright}shchik and A.B. Sossinsky and A.M. Verbovetsky",
booktitle = "The Diverse World of PDEs",
address = "United States",
}