Geodesic
On straightening the characteristics of a~quasilinear second-order equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 1, pp. 18-25

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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. 
@article{TMF_1988_75_1_a1,
     author = {F. Kh. Mukminov},
     title = {On straightening the characteristics of a~quasilinear second-order equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {18--25},
     publisher = {mathdoc},
     volume = {75},
     number = {1},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_1_a1/}
}
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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/