Explicit differential characterization of PDE systems pointwise equivalent to Y_{X^{j_1}X^{j_2}}=0, 1\leq j_1,j

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73417In this paper, a direct continuation of math.DG/0411165, we generalize S. Lie's linearization criterion of an ordinary second order differential equation to the case of several independent variables (x^1, x^2 ..., x^n), n >1, and a single dependent variable y. Strikingly, as in math.DG/0411165, the (complicated) characterizing differential system is of first order. By means of computer programming, this phenomenon was discovered in the case n=2 by S. Neut and M. Petitot (www.lifl.fr/~neut/recherche/these.pdf).24 pages, 0 figure; more referencesComplex VariablesDifferential Geometry58F36, 34A05, 58A15, 58A20, 58F36, 34C14, 32V40Explicit differential characterization of PDE systems pointwise equivalent to Y_{X^{j_1}X^{j_2}}=0, 1\leq j_1,j_2\leq n\geq 2text