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.
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