# Differential invariants of generic parabolic Monge–Ampère equations

@article{Ferraioli2006DifferentialIO, title={Differential invariants of generic parabolic Monge–Amp{\`e}re equations}, author={Diego Catalano Ferraioli and Alexandre M. Vinogradov}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2006}, volume={45} }

Some new results on the geometry of classical parabolic Monge–Ampère equations (PMAs) are presented. PMAs are either integrable, or non-integrable according to the integrability of its characteristic distribution. All integrable PMAs are locally equivalent to the equation uxx = 0. We study non-integrable PMAs by associating with each of them a one-dimensional distribution on the corresponding first-order jet manifold, called the directing distribution. According to some property of this…

## 14 Citations

### Normal forms for parabolic Monge-Ampere equations

- Mathematics
- 2007

We find normal forms for parabolic Monge-Ampere equations. Of these, the most general one holds for any equation admitting a complete integral. Moreover, we explicitly give the determining equation…

### Scalar differential invariants of symplectic Monge-Ampère equations

- Mathematics
- 2011

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…

### Scalar dierential invariants of symplectic Monge-Ampère equations

- Mathematics
- 2011

All second order scalar dierential invariants of symplectic hyperbolic and elliptic Monge‐Ampere equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that…

### On geometry of second-order parabolic equations in two independent variables

- Mathematics
- 2008

1 In this paper we announce some new results concerning second-order differential parabolic equation in two independent variables. Equations of Monge‐ Ampere type are distinguished among them. They…

### Contact Relative Differential Invariants for Non Generic Parabolic Monge-Ampère Equations

- Mathematics
- 2008

We find relative differential invariants of different orders for non generic parabolic Monge-Ampère equations (MAE’s). They are constructed in terms of some tensors associated with the derived flag…

### Partial extensions of jets and the polar distribution on Grassmannians of non-maximal integral elements

- Mathematics
- 2016

### ON THE POLAR DISTRIBUTION FOR SINGULARITIES EQUATIONS OF NONLINEAR PDES

- Mathematics
- 2012

In the beginning of this note we review the fundamentals of Grassmann and flag bundles, stressing their key role in the geometrical formalism of nonlinear PDEs. Then we observe that the equation of…

### Some remarks on contact manifolds, Monge-Ampere equations and solution singularities

- Mathematics
- 2014

We describe some natural relations connecting contact geometry, classical Monge-Ampere equations and theory of singularities of solutions to nonlinear PDEs. They reveal the hidden meaning of…

### Partial extensions of jets and the polar distribution on Grassmannians of non-maximal integral elements

- Mathematics
- 2014

### Non-maximal integral elements in jet spaces and partial prolongations

- Mathematics
- 2014

The space of non maximal $l$-dimensional horizontal integral elements at a point in a jet space as well as the space of $(l,n)$-dimensional flags of horizontal integral elements are supplied with a…

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