New Dubrovin-type integrability theory applications of differential rings / Orest D. Artemovych, Denis L. Blackmore, Radosław A. Kycia, Anatolij K. Prykarpatski // W: The Diverse World of PDEs Algebraic ... więcej

New Dubrovin-type integrability theory applications of differential rings / Orest D. Artemovych, Denis L. Blackmore, Radosław A. Kycia, Anatolij K. Prykarpatski // W: The Diverse World of PDEs Algebraic and Cohomological Aspects : Alexandre Vinogradov Memorial Conference Diffieties, Cohomological Physics, and Other Animals December 13–17, 2021 Independent Unversity of Moscow and Moscow State University, Moscow, Russia [Dokument elektroniczny] / eds. I.S. Krasil′shchik, A.B. Sossinsky, A.M. Verbovetsky. – Providence, Rhode Island : American Mathematical Society, 2023. – (Contemporary Mathematics, ISSN 0271-4132 ; Vol. 789). – S. 19-39. – Tryb dostępu: https://www.ams.org/books/conm/789/. – Bibliogr. 54 poz., Abstr. – On memoriam of the outstanding geometer Alexander Vinogradov, who opened new blooming faces of the theory of differential equations. – doi: 10.1090/conm/789/15838. – ISBN 978-1-4704-7409-6 (eBook). – ISBN 978-1-4704-7355-6 (Softcover)

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, ... więcej

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.