Contact relative differential invariants for non generic parabolic Monge-Ampère equations. (English) Zbl 1154.35004
In the present paper the classical problem of contact classification of Monge-Ampère equations is studied. This problem has a long history, starting with S. Lie, G. Darboux and E. Goursat, see the recent monograph [A. Kushner, V. Lychagin and V. Rubtsov, Contact geometry and nonlinear differential equations. Encyclopedia of Mathematics and Its Applications 101, Cambridge University Press (2007; Zbl 1122.53044)]. This paper is devoted to classification of parabolic equations. The authors characterize in terms of relative invariants when a parabolic Monge-Ampère equation can be brought to one of the forms \(z_{yy}=F(x,y,z,z_x,z_y)\) or \(z_{yy}-2zz_{xy}+z^2z_{xx}=G(x,y,z,z_x,z_y)\).
Reviewer: Boris S. Kruglikov (Tromsø)
MSC:
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35K55 | Nonlinear parabolic equations |
| 53A55 | Differential invariants (local theory), geometric objects |
| 58A20 | Jets in global analysis |
| 53D10 | Contact manifolds (general theory) |
Keywords:
Monge-Ampère equation; Parabolic PDE; Contact transformation; Relative differential invariantCitations:
Zbl 1122.53044References:
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