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@article{2330877,
author = {Artemovych, Orest and Blackmore, Denis L. and Kycia, Radoslaw Antoni and Prykarpatski, Anatolij K.},
article_location = {Providence, Rhode Island},
doi = {http://dx.doi.org/10.1090/conm/789/15838},
keywords = {differential geometry, differential algebra, differential equations, covering mappings, differential ideals},
language = {eng},
issn = {0271-4132},
journal = {Contemporary Mathematics},
title = {New Dubrovin-type integrability theory applications of differential rings},
url = {https://www.ams.org/books/conm/789/},
volume = {789},
year = {2023}
}
TY - JOUR
ID - 2330877
AU - Artemovych, Orest - Blackmore, Denis L. - Kycia, Radoslaw Antoni - Prykarpatski, Anatolij K.
PY - 2023
TI - New Dubrovin-type integrability theory applications of differential rings
JF - Contemporary Mathematics
VL - 789
SP - 19-39
EP - 19-39
PB - American Mathematical Society
SN - 02714132
KW - differential geometry, differential algebra, differential equations, covering mappings, differential ideals
UR - https://www.ams.org/books/conm/789/
N2 - We present a new and effective approach to studying differentialalgebraic relationships by means of specially constructed finitely-generated invariant subrings in differential rings. Based on their properties, we reanalyzed the Dubrovin integrability criterion for the Riemann type differentialfunctional constraints, perturbed by means of some elements from a suitably constructed differential ring. We also studied invariant finitely-generated ideals naturally related with constraints, generated by the corresponding Liealgebraic 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.
ER -
ARTEMOVYCH, Orest, Denis L. BLACKMORE, Radoslaw Antoni KYCIA and Anatolij K. PRYKARPATSKI. New Dubrovin-type integrability theory applications of differential rings. \textit{Contemporary Mathematics}. Providence, Rhode Island: American Mathematical Society, 2023, vol.~789, p.~19-39. ISSN~0271-4132. Available from: https://dx.doi.org/10.1090/conm/789/15838.
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