On the Equivalence of First-Order Abel Equations with Coefficients Depending on the Control Parameter

On the Equivalence of First-Order Abel Equations with Coefficients Depending on the Control Parameter

In this paper, we have found necessary and sufficient conditions under which two Abel equations with coefficients depending on a control parameter are locally equivalent with respect to the same pseudogroup of feedback transformations. These conditions are formulated in terms of differential invaria...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-07, Vol.248 (4), p.505-510
1. Verfasser: Shurygin, V. V.
Format: Artikel
Sprache:eng
Schlagworte:
Differential equations
Equivalence
Mathematical analysis
Mathematics
Mathematics and Statistics
Parameters
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Zusammenfassung:In this paper, we have found necessary and sufficient conditions under which two Abel equations with coefficients depending on a control parameter are locally equivalent with respect to the same pseudogroup of feedback transformations. These conditions are formulated in terms of differential invariants.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04891-1