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Marvan, Michal; Vinogradov, Alexandre M.; Yumaguzhin, Valery A.

Differential invariants of generic hyperbolic Monge-Ampère equations. (English) Zbl 1129.58015

Cent. Eur. J. Math. 5, No. 1, 105-133 (2007).
A hyperbolic Monge-Ampére equation is interpreted as a pair of 2-dimensional, skew-orthogonal, non-Lagrangian subdistributions of the contact distribution on a 5-dimensional contact manifold, see also [V. V. Lychagin, Russ. Math. Surv. 34, No. 1, 149–180 (1979); translation from Usp. Mat. Nauk 34, No.1(205), 137-165 (1979; Zbl 0405.58003); A. G. Kushner, Dokl. Math. 58, No. 1, 103–104 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 361, No. 5, 595–596 (1998; Zbl 0958.58002); O. P. Tchii, Lobachevskii J. Math. 4, 109–162, electronic only (1999; Zbl 0938.35011); V. B. Levenshtam, Dokl. Math. 72, No. 3, 872–875 (2005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 405, No. 2, 169–172 (2005; Zbl 1133.34344)]. Differential invariants are easily visible due to the existence of bicharacteristics. The equivalence problem is solved.
Reviewer: Maido Rahula (Tartu)

Cited in 5 Documents

MSC:

58J70 Invariance and symmetry properties for PDEs on manifolds
58J45 Hyperbolic equations on manifolds

Keywords:

Monge-Ampère equation; contact transformation; Frölicher-Nijenhuis bracket; scalar differential invariant

Citations:

Zbl 0427.58002; Zbl 0958.58002; Zbl 0938.35011; Zbl 1133.34344; Zbl 0405.58003
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References:

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