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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 2, Pages 195–220 (Mi izv76)  

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"

Abstract: 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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English version:
Izvestiya: Mathematics, 1996, 60:2, 425–451

Bibliographic databases:

UDC: 517.95
MSC: Primary 58G37, 58A30; Secondary 35G20
Received: 24.05.1995

Citation: 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
\by D.~V.~Tunitsky
\paper On the contact linearization of Monge--Ampere equations
\jour Izv. RAN. Ser. Mat.
\yr 1996
\vol 60
\issue 2
\pages 195--220
\jour Izv. Math.
\yr 1996
\vol 60
\issue 2
\pages 425--451

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    This publication is cited in the following articles:
    1. D. V. Tunitsky, “On the global solubility of the Monge–Ampere hyperbolic equations”, Izv. Math., 61:5 (1997), 1069–1111  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Tchij O.P., “Hyperbolic Monge-Ampere equations with transitive symmetry groups”, Doklady Akademii Nauk Belarusi, 42:2 (1998), 45–48  mathscinet  zmath  isi
    3. D. V. Tunitsky, “Monge–Ampére equations and characteristic connection functors”, Izv. Math., 65:6 (2001), 1243–1290  mathnet  crossref  crossref  mathscinet  zmath
    4. Ishikawa G., Morimoto T., “Solution surfaces of Monge-Ampere equations”, Differential Geometry and Its Applications, 14:2 (2001), 113–124  crossref  mathscinet  zmath  isi  scopus  scopus
    5. A. G. Kushner, “Almost product structures and Monge-Ampère equations”, Lobachevskii J. Math., 23 (2006), 151–181  mathnet  mathscinet  zmath
    6. A. G. Kushner, “Contact linearization of nondegenerate equations”, Russian Math. (Iz. VUZ), 52:4 (2008), 38–52  mathnet  crossref  mathscinet  zmath  elib
    7. Kushner, AG, “Transformation of hyperbolic Monge-Amp,re equations into linear equations with constant coefficients”, Doklady Mathematics, 78:3 (2008), 907  crossref  mathscinet  zmath  isi  elib  scopus
    8. Kushner, AG, “Contact Linearization of Monge-Ampere Equations and Laplace Invariants”, Doklady Mathematics, 78:2 (2008), 751  crossref  mathscinet  zmath  isi  elib  scopus
    9. Kushner A.G., “A contact linearization problem for Monge-Ampere equations and Laplace invariants”, Acta Applicandae Mathematicae, 101:1–3 (2008), 177–189  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. D. V. Tunitsky, “On some categories of Monge-Ampère systems of equations”, Sb. Math., 200:11 (2009), 1681–1714  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. D. V. Tunitsky, “Monge–Ampère equations and tensorial functors”, Izv. Math., 73:6 (2009), 1217–1263  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. 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  mathnet  elib
    13. Alonso-Blanco, R, “Normal forms for Lagrangian distributions on 5-dimensional contact manifolds”, Differential Geometry and Its Applications, 27:2 (2009), 212  crossref  mathscinet  zmath  isi  scopus
    14. Kushner A.G., “Classification of Monge-Ampere Equations”, Differential Equations: Geometry, Symmetries and Integrability - the Abel Symposium 2008, Abel Symposia, 5, 2009, 223–256  mathscinet  zmath  isi
    15. Kushner, AG, “On Contact Equivalence of Monge-AmpSre Equations to Linear Equations with Constant Coefficients”, Acta Applicandae Mathematicae, 109:1 (2010), 197  crossref  zmath  isi  scopus
    16. D. V. Tunitsky, “On the global solubility of the Cauchy problem for hyperbolic Monge–Ampére systems”, Izv. Math., 82:5 (2018), 1019–1075  mathnet  crossref  crossref  adsnasa  isi  elib
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