Geodesic
On straightening the characteristics of a quasilinear second-order equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 1, pp. 18-25 
F. Kh. Mukminov. On straightening the characteristics of a quasilinear second-order equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 1, pp. 18-25. http://geodesic.mathdoc.fr/item/TMF_1988_75_1_a1/
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     author = {F. Kh. Mukminov},
     title = {On straightening the characteristics of a~quasilinear second-order equation},
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     pages = {18--25},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_1_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

An invertible transformation that preserves the class of quasilinear second-order equations is proposed. Necessary and sufficient conditions are found under which this transformation carries a quasilinear equation into an equation with straight characteristics. For one quasilinear equation the general solution is found by means of the transformation. Examples of Lagrangians of the form $L(u,u_xu_y)$ possessing conservation laws of high order are given.

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