New Dubrovin-type integrability theory applications of differential rings
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Contemporary Mathematics |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.ams.org/books/conm/789/ |
| Doi | http://dx.doi.org/10.1090/conm/789/15838 |
| Keywords | differential geometry, differential algebra, differential equations, covering mappings, differential ideals |
| Description | 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. |
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