Cartan equivalence problem for third-order differential operators

Authors : Mehdi Nadjafikhah, Rohollah Bakhshandeh Chamazkoti

Pages : 949-958

Doi:10.3906/mat-1205-31

View : 14 | Download : 8

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :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.
Keywords : Differential operator, Cartan equivalence, gauge equivalence, invariant, pseudogroup, Lie algebra