Explicit differential characterization of PDE systems pointwise equivalent to Yₓʲ¹ₓʲ²=0, 1≤ j₁,j₂≤ n≥ 2

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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).