Geodesic
On the contact linearization of Monge–Ampere equations
Izvestiya. Mathematics, Tome 60 (1996) no. 2, pp. 425-451 
D. V. Tunitsky. On the contact linearization of Monge–Ampere equations. Izvestiya. Mathematics, Tome 60 (1996) no. 2, pp. 425-451. http://geodesic.mathdoc.fr/item/IM2_1996_60_2_a7/
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     title = {On the contact linearization of {Monge{\textendash}Ampere} equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to the solution of a number of problems related to the contact classification of Monge–Ampere equations with two independent variables. In the 1870s Sophus Lie formulated the problem of finding whether a local reduction of a given Monge–Ampere equation to some simpler second-order equation (to a semilinear, linear with respect to the derivatives, equation with constant coefficients) is possible. In this paper conditions are studied that yield a realization of such a reduction. As objects that occur in the formulation of these conditions, we use the characteristic bundles of the given Monge–Ampere equation and their derivatives.

[1] Lychagin V. V., “Kontaktnaya geometriya i nelineinye differentsialnye uravneniya vtorogo poryadka”, UMN, 34:1(205) (1979), 137–165 | MR | Zbl

[2] Tunitskii D. V., “Zadacha Koshi dlya giperbolicheskikh uravnenii Monzha–Ampera”, Izv. RAN. Ser. matem., 57:4 (1993), 174–191

[3] Morimoto T., “La géométrie des équations Monge–Ampère”, C. R. Acad. Sc. Paris. Série A, 289 (1979), 25–28 | MR | Zbl

[4] Lie S., Gesammelte Abhandlungen, Bd. 3, H. Aschehoug Co, Oslo; B. G. Teubner, Leipzig, 1922 | Zbl

[5] Goursat E., Leçons sur l'intégration des équations aux dérivées partielles du second ordre, V. 1, Hermann, Paris, 1896 | Zbl

[6] Lychagin V. V., Rubtsov V. N., “O teoremakh Sofusa Li dlya uravnenii Monzha–Ampera”, DAN BSSR, 27:5 (1983), 396–398 | MR | Zbl

[7] Lychagin V. V., Rubtsov V. N., Chekalov I. V., “A classification of Monge–Ampère equations”, Ann. scient. Éc. Norm. Sup. 4 série, 26 (1993), 281–308 | MR | Zbl

[8] Rashevskii P. K., Geometricheskaya teoriya uravnenii s chastnymi proizvodnymi, Gostekhizdat, M.–L., 1947

[9] Uorner F., Osnovy teorii gladkikh mnogoobrazii i grupp Li, Mir, M., 1987 | MR

[10] Khart N., Geometricheskoe kvantovanie v deistvii, Mir, M., 1985 | MR