This article is cited in 16 scientific papers (total in 16 papers)
On the contact linearization of Monge–Ampere equations
D. V. Tunitsky
International Center "Sophus Lie"
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.
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Izvestiya: Mathematics, 1996, 60:2, 425–451
MSC: Primary 58G37, 58A30; Secondary 35G20
D. V. Tunitsky, “On the contact linearization of Monge–Ampere equations”, Izv. RAN. Ser. Mat., 60:2 (1996), 195–220; Izv. Math., 60:2 (1996), 425–451
Citation in format AMSBIB
\paper On the contact linearization of Monge--Ampere equations
\jour Izv. RAN. Ser. Mat.
\jour Izv. Math.
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D. V. Tunitsky, “Monge–Ampére equations and characteristic connection functors”, Izv. Math., 65:6 (2001), 1243–1290
Ishikawa G., Morimoto T., “Solution surfaces of Monge-Ampere equations”, Differential Geometry and Its Applications, 14:2 (2001), 113–124
A. G. Kushner, “Almost product structures and Monge-Ampère equations”, Lobachevskii J. Math., 23 (2006), 151–181
A. G. Kushner, “Contact linearization of nondegenerate equations”, Russian Math. (Iz. VUZ), 52:4 (2008), 38–52
Kushner, AG, “Transformation of hyperbolic Monge-Amp,re equations into linear equations with constant coefficients”, Doklady Mathematics, 78:3 (2008), 907
Kushner, AG, “Contact Linearization of Monge-Ampere Equations and Laplace Invariants”, Doklady Mathematics, 78:2 (2008), 751
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D. V. Tunitsky, “On some categories of Monge-Ampère systems of equations”, Sb. Math., 200:11 (2009), 1681–1714
D. V. Tunitsky, “Monge–Ampère equations and tensorial functors”, Izv. Math., 73:6 (2009), 1217–1263
A. G. Kushner, “O privedenii uravnenii Monzha–Ampera k uravneniyu Eilera–Puassona”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 151, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2009, 60–71
Alonso-Blanco, R, “Normal forms for Lagrangian distributions on 5-dimensional contact manifolds”, Differential Geometry and Its Applications, 27:2 (2009), 212
Kushner A.G., “Classification of Monge-Ampere Equations”, Differential Equations: Geometry, Symmetries and Integrability - the Abel Symposium 2008, Abel Symposia, 5, 2009, 223–256
Kushner, AG, “On Contact Equivalence of Monge-AmpSre Equations to Linear Equations with Constant Coefficients”, Acta Applicandae Mathematicae, 109:1 (2010), 197
D. V. Tunitsky, “On the global solubility of the Cauchy problem for hyperbolic Monge–Ampére systems”, Izv. Math., 82:5 (2018), 1019–1075
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