Geodesic
The geometry of a~quasilinear system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 67-84

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The geometry of a system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables is studied by using the Cartan method of invariant forms and the group-theoretic method of extensions and enclosings due to G. F. Laptev (for finite groups) and A. M. Vasil'ev (for infinite groups). Systems of quasilinear equations with the first and second partial derivatives of two functions $u$ and $v$ in two independent variables $x$ and $y$ are classified. 
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     author = {L. N. Orlova},
     title = {The geometry of a~quasilinear system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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L. N. Orlova. The geometry of a~quasilinear system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 67-84. http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a7/