From Realization Lemma established by N. Tanaka, differential systems may be regarded as systems of first order differential equations. We characterize the geometric structure of systems of second order partial differential equations of several unknown functions in terms of differential systems and seek a system of equations the Lie algebra of all infinitesimal automorphisms of which is simple.
"Differential systems associated with partial differential equations of several unknown functions." Hokkaido Math. J. 46 (1) 41 - 86, February 2017. https://doi.org/10.14492/hokmj/1498788096