This article is dedicated to solving the equivalence problem for a pair of third-order differential operators on the line under general fiber-preserving transformation using the Cartan method of equivalence. We will treat 2 versions of equivalence problems: first, the direct equivalence problem, and second, an equivalence problem to determine conditions on 2 differential operators such that there exists a fiber-preserving transformation mapping one to the other according to gauge equivalence.
Differential operator, Cartan equivalence, gauge equivalence, invariant, pseudogroup, Lie algebra
NADJAFIKHAH, MEHDI and CHAMAZKOTI, ROHOLLAH BAKHSHANDEH
"Cartan equivalence problem for third-order differential operators,"
Turkish Journal of Mathematics: Vol. 37:
6, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss6/6