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… 

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