Geodesic
The Geometry of a Quasilinear System of Two Partial Differential Equations Containing the First and the Second Partial Derivatives of Two Functions in Two Independent Variables
Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 421-432

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The geometry of the system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables is studied by using Élie Cartan's method of invariant forms and the group-theoretic method of extensions and enclosings due to G. F. Laptev (for finite groups) and A. M. Vasilev (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.
Keywords: geometry of partial differential equations, quasilinear partial differential system, integral manifold, characteristic.
Mots-clés : point transformation group 
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     author = {L. N. Orlova},
     title = {The {Geometry} of a {Quasilinear} {System} of {Two} {Partial} {Differential} {Equations} {Containing} the {First} and the {Second} {Partial} {Derivatives} of {Two} {Functions} in {Two} {Independent} {Variables}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {421--432},
     publisher = {mathdoc},
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L. N. Orlova. The Geometry of a Quasilinear System of Two Partial Differential Equations Containing the First and the Second Partial Derivatives of Two Functions in Two Independent Variables. Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 421-432. http://geodesic.mathdoc.fr/item/MZM_2009_85_3_a9/