Explicit differential characterization of PDE systems pointwise equivalent to Y_X^j1X^j2=0, 1≤ j₁,j₂≤ n≥ 2

2004/11/29 by Joel Merker, Merker, Joel
Mathematics · #32V40 #34A05 #34C14 #58A15 #58A20 #58F36 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG #msc:32V40 #msc:34A05 #msc:34C14 #msc:58A15 #msc:58A20 #msc:58F36

paper · pdf · doi:10.48550/arxiv.math/0411637

24 pages, 0 figure; more references

arxiv created 2005/01/19 · arxiv updated 2009/12/01

Abstract

In 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 (x¹, x² ..., xⁿ), 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).

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