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1
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Differential invariants of generic hyperbolic Monge-Ampère equations

100%
Marvan M., Vinogradov A., Yumaguzhin V.
Open Mathematics
|
2007
|
tom 5
|
nr 1
105-133
EN
In this paper basic differential invariants of generic hyperbolic Monge-Ampère equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.
2
Content available remote

Scalar differential invariants of symplectic Monge-Ampère equations

100%
Paris A., Vinogradov A.
Open Mathematics
|
2011
|
tom 9
|
nr 4
731-751
EN
All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. We also introduce a series of invariant differential forms and vector fields which allow us to construct numerous scalar differential invariants of higher order. The introduced invariants give a solution of the symplectic equivalence of Monge-Ampère equations. As an example we study equations of the form u xy + f(x, y, u x, u y) = 0 and in particular find a simple linearization criterion.
3
Content available remote

Contact integrable extensions and differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation

76%
Morozov O.
Open Mathematics
|
2012
|
tom 10
|
nr 5
1688-1697
EN
The method of contact integrable extensions is used to find new differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation and corresponding Bäcklund transformations.
4
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Essential Killing fields of parabolic geometries: projective and conformal structures

64%
Čap A., Melnick K.
Open Mathematics
|
2013
|
tom 11
|
nr 12
2053-2061
EN
We use the general theory developed in our article [Čap A., Melnick K., Essential Killing fields of parabolic geometries, Indiana Univ. Math. J. (in press)], in the setting of parabolic geometries to reprove known results on special infinitesimal automorphisms of projective and conformal geometries.
5
Content available remote

The gap phenomenon in the dimension study of finite type systems

64%
Kruglikov B.
Open Mathematics
|
2012
|
tom 10
|
nr 5
1605-1618
EN
Several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case when the structure is associated to a vector distribution, is proposed.
6
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A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence

64%
Morozov O.
Open Mathematics
|
2014
|
tom 12
|
nr 2
271-283
EN
We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.
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