New Dubrovin-type integrability theory applications of
differential rings

J 2023

New Dubrovin-type integrability theory applications of differential rings

ARTEMOVYCH, Orest, Denis L. BLACKMORE, Radoslaw Antoni KYCIA a Anatolij K. PRYKARPATSKI

Základní údaje

Originální název

New Dubrovin-type integrability theory applications of differential rings

Autoři

ARTEMOVYCH, Orest, Denis L. BLACKMORE, Radoslaw Antoni KYCIA a Anatolij K. PRYKARPATSKI

Vydání

Contemporary Mathematics, Providence, Rhode Island, American Mathematical Society, 2023, 0271-4132

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10102 Applied mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1090/conm/789/15838

Klíčová slova anglicky

differential geometry, differential algebra, differential equations, covering mappings, differential ideals

Štítky

RIV ne

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 28. 10. 2023 13:00, Radoslaw Antoni Kycia, Ph.D.

Anotace

V originále

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.

Návaznosti

MUNI/A/1099/2022, interní kód MU

Název: Specifický výzkum v odborné a učitelské matematice 2023

Investor: Masarykova univerzita, Specifický výzkum v odborné a učitelské matematice 2023

Citovat

ARTEMOVYCH, Orest, Denis L. BLACKMORE, Radoslaw Antoni KYCIA a Anatolij K. PRYKARPATSKI. New Dubrovin-type integrability theory applications of differential rings. Contemporary Mathematics. Providence, Rhode Island: American Mathematical Society, 2023, roč. 789, s. 19-39. ISSN 0271-4132. Dostupné z: https://dx.doi.org/10.1090/conm/789/15838.

@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 a Anatolij K. PRYKARPATSKI. New Dubrovin-type integrability theory applications of differential rings. \textit{Contemporary Mathematics}. Providence, Rhode Island: American Mathematical Society, 2023, roč.~789, s.~19-39. ISSN~0271-4132. Dostupné z: https://dx.doi.org/10.1090/conm/789/15838.

Podrobný výpis o publikaci